HCF & LCM, General Mathematics

Question: The greatest number that will divide 187, 233 and 279 leaving the same remainder in each case is :
A
30

B
36

C
46

D
56

Note: solution: Required number = H.C.F. of (233-187),(279-233) & (279-187) = H.C.F. of 46,46 & 92 =46.
1. Report
Question: The greatest number which can divide 1356, 1868 and 2764 leaving the same remainder 12 in each case, is :
A
64

B
124

C
156

D
260

Note: solution: Required number =H.C.F. of (1356-12),(1860-12) & (2764-12) =H.C.F. of 1344, 1856 & 2752 = 64.
1. Report
Question: The greatest number by which is 1657 and 2037 are divided to give remainders 6 and 5 respectively, is ;
A
127

B
123

C
235

D
305

Note: solution: Required number = H.C.F. of (1657-6) & (2037-5) = H.C.F. of 1651 & 2032 =127.
1. Report
Question: The greatest possible length which can be used to measure exactly the lengths 4 m 95 cm is :
A
15 cm

B
25 cm

C
35 cm

D
45 cm

Note: solution: Required length = H.C.F. of 900 cm, 495 cm =45 cm.
1. Report
Question: Three different containers contain 496 litres, 43 litres and 713 litres of mixtures of milk and water respectively. What biggest measure can measure all the different quantities exactly ?
A
1 litre

B
7 litres

C
31 litres

D
41 litres

Note: solution: Required measurement = H.C.F. of 496,403 & 713 litres = 31 litres.
1. Report
Question: The least number which is a perfect square and is divisible by each of the numbers 16, 20 and 24, is :
A
1600

B
3600

C
6400

D
1440

Note: solution: The least number divisible by `16, 20, 24 = 1 c.m. of 16, 20, 24 =240 = 2 xx 2 xx 2 xx 2 xx 3 xx 5` To make it a perfect square, it must be multiplied by `3 xx 5`. `:.` Required number= `240 xx 3 xx 5 = 3600`.
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Question: What is the least number which when divided by 8,9,12 and 15 leaves the same remainder 1 in each case ?
A
179

B
181

C
359

D
361

Note: solution: Required number = `(1 c.m. of 8, 9, 12, 15) + 1 = 361`.
1. Report
Question: What is the greatest number of three digits which when divided by 6, 9 and 12 leaves a remainder of 3 in each case ?
A
975

B
996

C
939

D
903

Note: solution: Greatest number of 3 digits is 999. L.C.M. of `6, 9 and 12 =36`. On dividing 999 by 36, remainder obtained is 27. `:.` Greatest number of 3 digits divisible by `6, 9, 12 = (999 - 27) = 972`. `:.` Required number = `(972 + 30) = 975`.
1. Report
Question: The least number of five digits which is exactly divisible by 12, 15 and 18 is :
A
10010

B
10015

C
10020

D
10080

Note: solution: Least number of 5 digits is 10000. L.C.M. of `12, 15, 18 is 180`. On dividing 10000 by 180, the remainder is 100. `:.` Required number = `10000+(180 - 100) = 10080`.
1. Report
Question: The smallest number which when diminished by 3 is divisible by 21, 28, 36 and 45 is :
A
423

B
1257

C
1263

D
1260

Note: solution: Required number = `(1.c.m. of 21, 28, 36, 45) +3 = 1263`.
1. Report

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Question: The greatest number that will divide 187, 233 and 279 leaving the same remainder in each case is :

Question: The greatest number which can divide 1356, 1868 and 2764 leaving the same remainder 12 in each case, is :

Question: The greatest number by which is 1657 and 2037 are divided to give remainders 6 and 5 respectively, is ;

Question: The greatest possible length which can be used to measure exactly the lengths 4 m 95 cm is :

Question: Three different containers contain 496 litres, 43 litres and 713 litres of mixtures of milk and water respectively. What biggest measure can measure all the different quantities exactly ?

Question: The least number which is a perfect square and is divisible by each of the numbers 16, 20 and 24, is :

Question: What is the least number which when divided by 8,9,12 and 15 leaves the same remainder 1 in each case ?

Question: What is the greatest number of three digits which when divided by 6, 9 and 12 leaves a remainder of 3 in each case ?

Question: The least number of five digits which is exactly divisible by 12, 15 and 18 is :

Question: The smallest number which when diminished by 3 is divisible by 21, 28, 36 and 45 is :