Method and examples
HCF_LCM
1. The HCF of two numbers is 14 and their LCM is 11592 . If one of the numbers is 504 , find the other?
2. Find the largest number which can exactly divide 513,783,1107 .
3. Find the smallest number exactly divisible by 12,15,20,27 .
4. Find the least number which when divided by 6,7, 8, 9,12 leaves the same remainder 2 in each case.
5. Find the largest number which divides 77 , 147 , 252 to leave the same remainder in each case.
6. Greatest number which can divide 1354 , 1806 , 2762 leaving the same remainder 10 in each case.
7. The greatest number that will divide 1657 , 2772 leaving respectively 6 , 5 as remainder.
8. The greatest number that will divide 290 , 460 , 552 leaving respectively 4 , 5 , 6 as remainder.
9. The product of HCF and LCM of 18 and 16 is
10. LCM of two numbers is 14 times their HCF. The sum of LCM and HCF is 600 . If one number is 280 , then find the other number ?
11. Find the least number which is exactly divided by 28,36,45 when we add 19 to it
Problem 7 of 11
7. The greatest number that will divide , leaving respectively , as remainder.

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HCF_LCM
7. The greatest number that will divide 1657 , 2772 leaving respectively 6 , 5 as remainder. The number divides 1657 and leaves 6 as remainder `:.` The number exactly divides 1657 - 6 = 1651 The number divides 2772 and leaves 5 as remainder `:.` The number exactly divides 2772 - 5 = 2767 Now, we have to find HCF of `1651, 2767` Find HCF of (1651,2767) 1651 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |

`:.` HCF of given numbers (1651,2767) = 1 `:.` Required number = HCF of `1651, 2767 = 1`.