June 4, 2018

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
lcm and hcf
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
lcm and hcf example
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
lcm hcf example
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
lcm and hcf
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.


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