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12 June, 13:10

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.

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  1. 12 June, 15:45
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    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
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