two numbers have these properties both numbers are greater than 6 the highest common factor is 6 the lowest common multiple is 60 find the two numbers

12 and 30 are two such given numbers.

Step-by-step explanation:

Here, given the LCM of both the numbers = 60

The HCF of both the number = 6

Both number are greater then 6.

Now, as we know LCM x HCF = Product of Two Numbers

⇒ 60 x 6 = 360 = Product of both numbers

Now, by the prime factorization of 360, we get:

360 = 2 x 2 x 2 x 3 x 3 x 5 = 12 x 30

Here, checking for the conditions:

(a) Both numbers 12, 30 are greater than 6

(b) HCF of 12 and 30 = 6

(c) LCM of 12 and 30 = 60

Hence, 12 and 30 are two such given numbers.