HCF and LCM: the ladder method

The Maths Habit

Which prime is a factor of both?

  1. 14 and 21

    7

  2. 10 and 25

    5

  3. 6 and 15

    3

Common factor
A number that is a factor of both numbers.
Highest common factor (HCF)
The biggest number that is a factor of both numbers.
Common multiple
A number that is a multiple of both numbers.
Lowest common multiple (LCM)
The smallest number that is a multiple of both numbers.

Find the HCF of 30 and 42.

230423152157
HCF =2×3=6

Find the HCF of 40 and 60.

24060220305101523
HCF =2×2×5=20

Find the HCF of 30 and 42.

230423152157
HCF =2×3=6

Find the HCF of 18 and 45.

31845361525
HCF =9

HCF and LCM: the ladder method worksheet, HCF, questions 1 to 8

Find the HCF and LCM of 12 and 18.

2121836923
HCF =2×3=6
LCM =6×2×3=36

Find the HCF and LCM of 30 and 45.

330455101523
HCF =3×5=15
LCM =15×2×3=90

Find the HCF and LCM of 12 and 18.

2121836923
HCF =2×3=6
LCM =6×2×3=36

Find the HCF and LCM of 16 and 24.

21624281224623
HCF =8
LCM =48

Find the HCF and LCM of 12 and 18.

2121836923
HCF =2×3=6
LCM =6×2×3=36

Find the HCF and LCM of 15 and 25.

5152535
HCF =5
LCM =75

Find the HCF and LCM of 12 and 18.

2121836923
HCF =2×3=6
LCM =6×2×3=36

Find the HCF and LCM of 9 and 36.

3936331214
HCF =9
LCM =36

Find the HCF and LCM of 12 and 18.

2121836923
HCF =2×3=6
LCM =6×2×3=36

Find the HCF and LCM of 28 and 42.

228427142123
HCF =14
LCM =84

HCF and LCM: the ladder method worksheet, LCM, questions 9 to 16

Answer sheet

Always, sometimes or never?

  1. The HCF of two numbers is smaller than both of them.

    Sometimes: 12 and 48

  2. The LCM of two numbers is the two numbers multiplied together.

    Sometimes: 4 and 6

  3. HCF × LCM is the two numbers multiplied together.

    Always

  4. The LCM is a multiple of the HCF.

    Always

  1. Use a ladder to find the HCF of 24, 36 and 60. The prime must be a factor of all three.

    12

  2. A ferry leaves every 15 minutes and a water taxi every 20 minutes. Both leave at 9:00. When do they next leave together?

    10:00

  3. Two numbers have an HCF of 6 and an LCM of 36. What could the two numbers be?

    12 and 18

  1. Use a ladder to find the HCF of 36 and 60.

    12

  2. Use a ladder to find the LCM of 20 and 30.

    60

  3. A ladder has 2 and 5 down the side and 3 and 7 at the bottom. What were the two numbers?

    30 and 70
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