Two numbers have these properties:
-Both numbers are greater than 6
-Their hcf is 6
-Their lcm is 60
What are the two numbers?

The highest common factor of two numbers is the largest whole number which is a factor of both, the HCF of 4 and 6 is 2 because the factors of 4 are 1, 2, 4 and the factors of 6 are 1, 2, 3, 6; the common factors are 1, 2 and the greatest is 2 so the highest common factor of 4 , 6 is 2
The least common multiple of two numbers is the smallest number that they both divide evenly into, the least common multiple of 4 and 6 is 12 because the multiples of 4 are 4, 8, 12, 16, ... and the multiples of 6 are 6, 12, 18, 24, ...; the first common multiple between then is 12

∵ Both numbers are greater than 6

∵ Their HCF is 6

- That means 6 is a factor of both of them

∴ The two numbers are multiple of 6 without any other common

factor greater than 6

Let us write the multiple of 6 greater than 6

∵ 12 , 18 , 24 , 30 , 36 , ......... are multiples of 6

∵ Their LCM is 60

- That means 60 can divided by them

∵ 60 can divided by 12

∵ 60 can divided by 30

∵ The factors of 12 are 1 , 2 , 3 , 4 , 6 , 12

∵ The factor of 30 are 1 , 2 , 3 , 5 , 6 , 10 , 15 , 30

∵ Their common factors are 1 , 2 , 3 , 6 and the greatest one is 6

- 12 and 30 have HCF of 6 and LCM of 60

∴ The two numbers are 12 and 30

The two numbers are 12 and 30

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