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 6 of 11
6. Greatest number which can divide , , leaving the same remainder in each case.

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HCF_LCM
6. Greatest number which can divide 1354 , 1806 , 2762 leaving the same remainder 10 in each case. The number divides 1354 and leaves 10 as remainder `:.` The number exactly divides 1354 - 10 = 1344 The number divides 1806 and leaves 10 as remainder `:.` The number exactly divides 1806 - 10 = 1796 The number divides 2762 and leaves 10 as remainder `:.` The number exactly divides 2762 - 10 = 2752 Now, we have to find HCF of `1344, 1796, 2752` Find HCF of (1344,1796) 1344 | | | | | | | | | | | | | | | | | | | | | | | | | | |

HCF of (1344, 1796) = 4 Now find HCF of (4,2752) HCF of (4, 2752) = 4 `:.` HCF of given numbers (1344,1796,2752) = 4 `:.` Required number = HCF of `1344, 1796, 2752 = 4`.