Question

Martin thinks of two numbers. He says, "The Highest Common Factor (HCF) of my two numbers is 6 The Lowest Common Multiple (LCM) of my two numbers is a multiple of 15" Write down two possible numbers that Martin is thinking of.

Answer 1

Answer:

30, 42

Step-by-step explanation:

"The Highest Common Factor (HCF) of my two numbers is 6"

The only factors the two numbers have in common are 2 and 3. Each number must have 2 and 3 as factors.

first number = 2 * 3 * ...

second number = 2 * 3 * ...

Since both numbers contain a 2 as a factor, both numbers must be even. The lowest common multiple is a multiple of 15, but it must be an even multiple of 15.

Multiples of 15: 15, 30, 45, 60, 75, 90, ...

We are interested only in the even multiples of 15: 30, 60, 90, ...

first number = 2 * 3 * 5 = 30

second number = 2 * 3 * 7 = 42

Example: 30, 42