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 10 of 11
10. LCM of two numbers is times their HCF. The sum of LCM and HCF is . If one number is , then find the other number ?

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HCF_LCM
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 ? `"LCM" = 14" HCF"` `"LCM + HCF " = 600` `=> 14 " HCF + HCF " = 600` `=> 15 " HCF " = 600` `=> "HCF " = 600 / 15 = 40` Here, `"LCM" = 14 " HCF"` `:. "LCM " = 14 * 40 = 560`. `:. "Other number " = ( "HCF" * "LCM" ) / ("Given number"} = ( 40 * 560 ) / 280 = 80`.