Question

Natasha calculated the L.C.M and H.C.F of two numbers. The L.C.M is 60 and the H.C.F is 3. If one of the numbers is 12 what is the other number? Use the Euclid method to show your line of reasoning.

Answer 1

As the least common multiple of two numbers is 60 , the two numbers are factors of 60 . Among {1,2,3,4,5,6,10,12,15,20,30,60} , 3 & 10 and 5 & 12 are the only two pair of numbers whose difference is 7 . But Least common multiple of 3 and 10 is 30 .

Answer 2

x×y = lcm×hcf

12×y = 3 × 60

then y = 3×60/12= 15