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 5 of 11
5. Find the largest number which divides , , to leave the same remainder in each case.

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HCF_LCM
5. Find the largest number which divides 77 , 147 , 252 to leave the same remainder in each case. `"Required number" = "HCF of " ( 147 - 77 ), ( 252 - 147 ), ( 252 - 77 )` `= "HCF of " 70, 105, 175 = 35`. Factor of 70,105,175 are as follows... 70 = 2 × 5 × 7 105 = 3 × 5 × 7 175 = 5 × 5 × 7 HCF = 5 × 7 = 35 HCF of `70,105,175` is `35`