Prime Factors, HCF & LCM (Cambridge International IGCSE Mathematics): Exam Questions

Write 220 as the product of its prime factors.

Find the highest odd number that is a factor of 60 and a factor of 90.

Find the lowest common multiple (LCM) of 8 and 14.

Write 54 as a product of its prime factors.

Write 18 as the product of its prime factors.

Find the lowest common multiple (LCM) of 15 and 27.

Write 825 as the product of its prime factors.

Find the lowest common multiple (LCM) of 48 and 60.

Write 195 as a product of its prime factors.

i) Write 60 as a product of its prime factors.

ii) Find the lowest common multiple (LCM) of 36 and 60.

Write 432 as the product of its prime factors.

Find the highest common factor (HCF) of 24 and 108.

Find the highest common factor (HCF) of 90 and 48.

Find the lowest common multiple (LCM) of 28 and 35.

Find the highest common factor of 48 and 80.

Find the lowest common multiple of 24 and 18.

Find the lowest common multiple (LCM) and highest common factor (HCF) of 20 and 15.

At a bus stop

• a red bus arrives every 18 minutes

and

• a blue bus arrives every 24 minutes.

At 1047 a red bus and a blue bus arrive.

Find the next time when a red bus and a blue bus arrive together.

Find the highest common factor (HCF) of 126 and 180.

i) Find the highest common factor (HCF) of 36 and 90.

ii) Find the lowest common multiple (LCM) of 36 and 90.

Gerry and Alain run around a running track.

To run around the track once

• Gerry always takes 90 seconds
• Alain always takes 105 seconds.

They start together at the same point.

After how many minutes are they next together at that point?

........................................ min

i) Find the highest common factor (HCF) of 28 and 98.

ii) Find the lowest common multiple (LCM) of 28 and 98.

Talan completes one lap of a track every 80 seconds.

i) Work out how many laps he can complete in one hour.

ii) Naima completes one lap of the same track every 88 seconds. Talan and Naima start running from point $A$ on the track at the same time. They each complete a number of laps of the track.

Work out the smallest number of laps they each complete before they are both at point $A$ again at the same time.

Talan completes ................. laps and Naima completes ................. laps. [3]

The number $N$ is written as a product of its prime factors.

$N=2^{5}\times7^{2}$

Work out the value of $N$.

Extract:

The number N is written as a product of its prime factors.

N = 2^5 × 7^2

Find the highest common factor (HCF) of 168 and $N$.

Extract:

The number N is written as a product of its prime factors.

N = 2^5 × 7^2

168 = 2 × 2 × 2 × 3 × 7

and N = 2 × 2 × 2 × 2 × 2 × 7 × 7

Make a 'factors Venn diagram' for these two numbers: '168 circle only' has 3, middle overlap has 2, 2, 2, 7, 'N circle only' has 2, 2, 7.

Find the lowest common multiple (LCM) of 168 and $N$.