HCF and LCM

• Find the largest number which divide 1356, 1868 and 2764 leaving the same remainder in each case.

Ans: From the Solution Methods the required number is,
HCF of (1868-1356), (2764-1356) and (2764-1868)
HCF of 512, 1408 and 896

So the HCF = 8*8 = 64. Since there are only two 8s in common.

• Find the greatest number that divides 130, 305 and 245 leaving remainders 6, 9 and 17 respectively.

Ans: From the Solution Methods required number is,
HCF of [(130-6), (305-9), (245-17)]
HCF of 124, 296, 228

So the HCF is 4.

• Find the number which when divided by 12, 16 and 18 leaves 5 as remainder in each case.

Ans: From the Solution Methods we see that,

(LCM of 12, 16, 18) + 5

So LCM = 2*2*3*4*3 = 144

Required number is 144 + 5 = 149.

• Find the largest possible number of 5 digits which is exactly divisible by 32, 36 and 40.

Ans: From the Solution Methods we see that,

LCM of 32, 36 and 40 = 1440.

The greatest 6 digit number is 99999

So the required number = 9999-639 = 99360.

• Find the greatest 4 digit number which when divided by 10, 15, 21 and 28 leaving remainders 4, 9, 15 and 22.

Ans: From the Solution Methods we get,

LCM of 10, 15, 21 and 28 = 420.

The largest 4 digit number is 9999

So four digit number divisible by 10, 15, 21 and 28 = 9999-339 = 9660.

Also k = 10-4 = 15-9= 21-15= 28-22 = 6

Required number is 9660-6 = 9654.