HCF - LCM Q.1 Finding the HCF by long division method the se- quence of quotient from top to bottom is 3, 1, 3 and the last divisor is 6. Find the sum of both the numbers ?

yEch Hkkx fof/k }kjk 𝐻𝐶𝐹 ¼e-l-i-½ fudkyrs le; Åij ls

uhps HkkxQy dk Øe 3] 1] 3 gS vkSj vkf[kjh Hkktd 6 gSA

nksuksa la[;kvksa dk ;ksx Kkr djks \

Q.2 Finding the HCF by long division method of two no's the sequence of quotient from top to bottom is 9, 8, 5 and the last divisor is 16. Find the sum of two no's ?

yEch Hkkx fof/k }kjk e-l-i- fudkyrs le; Åij ls uhps

HkkxQy dk Øe 9] 8] 5 gSA vkSj vkf[kjh Hkktd 16 gS nksuksa

la[;kvksa dk ;ksx Kkr djks \

Q.3 Finding the HCF by long division method of two numbers the sequence of quotient from top to bottom is 2, 2 & 13 and the last division is 35. Find both the numbers ?

yEch Hkkx fof/k }kjk e-l-i- fudkyrs le; Åij ls uhps

HkkxQy dk Øe 2] 2] 13 gS vkSj vkf[kjh Hkktd 35 gSA

nksuksa la[;k,¡ Kkr djks \

Q.4 Find HCF of 72 & 90 ?

72 o 90 dk e-l-i- (𝐻𝐶𝐹) Kkr djks \

Q.5 HCF of 48, 90, 120 ?

48] 90] 120 dk e-l-i- Kkr djks \

Q.6 Find HCF of 216, 423, 1215, 1422, 2169, 2223,

216] 423] 1215] 1422] 2169] 2223] dk e-l-i- Kkr djks \

Q.7 There are three prime numbers, the product of 1 st two no. is 1891 and the product of last two no. is 7991. Find all the numbers ?

rhu vHkkT; la[;k,¡ gSA igyh nks la[;kvksa dk xq.kuQy

1891 o vkf[kjh nks dk xq.kuQy 7991 gSA rc rhuksa la[;k,¡

Kkr djks \

Q.8 Find the largest no. of two digit which upon divi- ded to 211 and 396 gives same remainder ?

nks vadksa dh cM+h ls cM+h la[;k Kkr djks ftlesa 211 o 396

dks Hkkx nsus ij leku 'ks"kQy cps \

Q.9 Find the greatest no. which when divided to 410, 751 and 1030 gives same remainder ?

og cM+h ls cM+h la[;k Kkr djks ftlesa 410] 751 o 1030

dks Hkkx nsus ij leku 'ks"kQy cps \

Q.10 A farmer has 945 cows and 2475 buffallo. He wants to graze them in minimum no. of groups in such a way that each group has only one type of animal and also contains equal no. of animals in each group. Find such minimum no. of groups ?

,d fdlku ds ikl 945 xk; o 2475 HkSalsa gSA og mudks

U;wure lewgksa esa bl izdkj pjkuk pkgrk gS fd izR;sd lewg

esa ,d gh izdkj dk tkuoj gks o izR;sd lewg esa tkuojksa

dh la[;k leku gksA lewgksa dh la[;k D;k gksxh \

Q.11 A gardner has 44 apple tree, 66 banana tree and 110 mango tree. He want to plant them in rows such a way that each row contain only one type of plant and also has equal no. of plants. Find no minimum rows ?

fdlh ekyh ds ikl 44 lsc ds 66 dsys ds vkSj 110 vke

ds isM+ gSA og mudks iafDr;ksa esa bl izdkj yxkuk pkgrk

gS fd izR;sd iafDr esa ,d gh izdkj ds isM+ gks o lHkh

iafDr;ksa esa isM+ksa dh la[;k leku gksA U;wure iafDr;k¡

Kkr djks \

Q.12 The area of three field are 288 cm2, 408 cm

2,

552cm2. Equal minimum size block are made

in the field. If the width of each rectangular block is 4 cm. Find its length ?

rhu [ksyksa dk {ks=Qy 288 ls-eh-2] 408 ls-eh-

2] 552 ls-eh

-2

gSA [ksr esa U;wure vkdkj ds leku xM~<s [kksns x,A ;fn

vk;krdkj xM~<s dh pkSM+kbZ 4 ls-eh- gS rks bldh yackbZ

Kkr djks \

Q.13 Find the least no. of equal size square tiles which can be fitted in a rectangular field whose sides are 284 m × 248 m ?

fdlh vk;rkdkj [ksr dk vkdkj 284 m × 248 m gSA bl

[ksr esa yxus okyh de ls de oxkZdkj Vkbyksa dh la[;k

Kkr djks \

Q.14 The ratio of two no is 3:4 and their LCM is 60 find their HCF ?

nks la[;kvksa dk vuqikr 3%4 gS vkSj mudk 𝐿𝐶𝑀 60 gSA

mudk e-l-o- (𝐻𝐶𝐹) Kkr djks \

Q.15 The sum of two no is 36 and their HCF is 4. Find the possible no. of pairs ?

nks la[;kvksa dk ;ksx 36 o mudk 𝐻𝐶𝐹 4 gS tksM+ksa dh

la[;k Kkr djks \

Q.16 The LCM of 4 no.s is 117 and the HCF of each pair is 3 find the multiplication of all the numbers

4 la[;kvksa dk y-l-o- 117 o izR;sd tksM+s dk e-l-i- 3 gSA

lHkh la[;kvksa dk xq.kuQy Kkr djks \

Q.17 The LCM and HCF of two consecutive even num -ber is 84 and 2. Find the sum of reciprocal of these two numbers ?

fdlh nks Øekxr le la[;kvksa dk y-l-o- vkSj e-l-o

Øe'k% 84 o 2 gSA bu la[;kvksa ds O;qDØeksa dk ;ksx Kkr djks \

Q.18 The sum and LCM of two number's are 156 and 504. Find both the numbers ?

nks la[;vksa dk ;ksx o y-l-o- 156 o 504 gSA nksuksa

la[;k,aas Kkr djks \

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Q.19 The sum and LCM of two number is 132 and 360 find two number's ?

nks la[;kvksa dk ;ksx o mudk y-l-o- 132 o 360 gSA

la[;k,sa Kkr djks \

Q.20 The HCF of two number is 11 and their LCM 693 If one number is 77. Find the other number?

nks la[;kvksa dk e-l-o-11 o y-l-i- 693 gSA ;fn ,d

la[;k 77 gS] rks nwljh la[;k Kkr djks \

Q.21 The LCM of two number is 12 times of HCF. The sum of HCF and LCM is 403. If both number are smaller than LCM. Find both the number ?

nks la[;kvksa dk 𝐿𝐶𝑀 muds 𝐻𝐶𝐹 dk 12 xquk gSA 𝐻𝐶𝐹 o

𝐿𝐶𝑀 dk ;ksx 403 gSA ;fn nksuksa la[;k,¡ 𝐿𝐶𝑀 ls NksVh gS]

rks la[;k,sa Kkr djks \

Q.22 The sum and difference of HCF and LCM of two number is 592 and 518. Find both the numbers if sum of these two number's is 296 ?

nks la[;kvksa ds 𝐻𝐶𝐹 o 𝐿𝐶𝑀 dk ;ksx o varj Øe'k% 592

vkSj 518 gSA ;fn nksuksa la[;kvksa dk ;ksx 296 gS rks la[;k,sa

Kkr djks \

Q.23 Find the smallest number which when divided by 5, 6, 8, and a gives remainder 3 in each case.

og NksVh ls NksVh la[;k Kkr djks] ftldks 5] 6] 8 o 9

ls Hkkx nsus ij 'ks"kQy 3 cprk gS \

Q.24 If a farmer pack 5 or 6 oranges in each box, he is left with 3 oranges. but if he pack 8 or 9 oranges in each box, he is left with 3 oranges. Find the number of oranges that he had ?

;fn ,d fdlku izR;sd cDls esa 5 ;k 6 larjs Hkjs] rks mlds

ikl 3 larjs cprs gSA ijarq ;fn og izR;sd cDls esa 8 ;k

9 larjs Hkjsa] rks mlds ikl 3 larjs cprs gSaA dqy larjksa

dh la[;k Kkr djks \

Q.25 Find the smallest number which when divided by 20, 25, 35 and 40 gives remainder 14, 19, 29 and 34

? og NksVh ls NksVh la[;k Kkr djks ftls 20] 25] 35 o 40

ls Hkkx nsus ij 14] 19] 20 o 34 'ks"kQy cps \

Q.26 Find the smallest number which when divided by 5, 6, 7 and 8 gives remainder 3 in each case. But it exactly divided by 9 ?

og NksVh ls NksVh la[;k Kkr djks] tks 9 ls Hkkx gksrh gS

rFkk 5] 6] 7] 8 ls Hkkx nsus ij gj ckj 3 'ks"k vkrk gS \

Q.27 Find the smallest number which when divided by 3, 4, 5 and 6 gives remainder 2, 3, 4 and 5. but exactly divide by 7 ?

og NksVh ls NksVh la[;k Kkr djks] tks 7 ls Hkkx gksrh gS rFkk 3]

4] 5] 6 ls Hkkx nsus ij Øe'k% 2] 3] 4 o 5 'ks"kQy cprk gS \

Q.28 Find the least multiple of 13 which when divided by 3, 4, 5 and 6 gives remainder 1, 2, 3 and 4 and

13 dk lcls NksVk xq.kkad Kkr djks ftldks 3] 4] 5 o 6

ls Hkkx nsus ij Øe'k% 1] 2] 3] 4 o 5 'ks"k cprk gS \

Q.29 Find the smallest number of 6 digit which when divided by 3, 4, 5, and 6 gives remainder 2 ?

6 vadksa dh NksVh ls NksVh la[;k Kkr djks ftldks 3] 4] 5

o 6 ls Hkkx nsus ij 2 'ks"kQy cprk gS \

Q.30 Find the largest number of 6 digit which when divided by 3, 4, 5, 6 and 8 gives remainder 1, 2, 3, 4 and 6 ?

6 vadksa dh og cM+h ls cM+h la[;k Kkr djks ftls 3] 4] 5]

o 8 ls Hkkx nsus ij Øe'k% 1] 2] 3] 4 o 6 'ks"k cprk gS \

Q.31 Find the least perfect square no. Which when divided by 4, 5, 6 gives remainder zero ?

og NksVh ls NksVh iw.kZ la[;k Kkr djks ftls 4] 5] 6 ls

Hkkx nsus ij 0 'ks"k cprk gS \

Q.32 Two cog wheels having 16 and 24 teeth respect ively. The bigger wheel makes 5 revolutions per hour. Calculate how many times the specific teeth of bigger wheel meets with the specific teeth of smaller wheel in 11 hours ?

nks nkarsnkj ifg;ksa esa 16 vkSj 24 nkar gSA cM+k ifg;k ,d

?kaVs esa 5 pDdj yxkrk gSA Kkr djks fd 11 ?kaVs esa cM+s

ifg;s dk dksbZ fuf'pr nkar NksVs ifg;s ds fuf'pr nkar ls

fdruh ckj feysxk \

Q.33 Three runners A, B and C run along a circular path of 12 km long with speeds 3 km/hr, 7km/hr, 13 km/hr. They start their race the same point for the same destination. After how much time they will meet again ?

3 /kkod 𝐴,𝐵,𝐶 12 𝑘𝑚. ds o`Ùkkdkj jkLrs ij Øe'k% 3 fd-

eh-@?kaVk] 7 fd-eh-@?kaVk o 13 fd-eh-@?kaVk dh pky ls

nkSM+ yxkrs gSaA os ,d txg ls ,d gh le; ij fdlh

,d fuf'pr txg ds fy, nkSM+uk 'kq: djrs gSaA os nksckjk

fdrus le; ckn feysaxs \

Q.34 4 bell rings at an interval of 12 sec, 15 sec, 20 sec, and 30 sec resp. How much time will they ring together in 6 hours ?

4 ?kfV;k¡ Øe'k% 12] 15] 20 o 30 lsd.M ds vUrjky ij

ctrh gSA os 6 ?kaVs esa fdruh ckj ,d lkFk ctsxh \

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