ii)

Calculate 504 as a product of it's prime factors.

$504 = 2^{3} \times 3^{2} \times 7$

[1]

The lowest common multiple of 84 and $N$ is the product of factors that exist in either list, ignoring repeats.

Compare the prime factors of 84 and 504, to identify the prime factors of $N$ .

$504 = 2^{3} \times 3^{2} \times 7 84 = 2^{2} \times 3 \times 7$

As 504 has prime factors of 2³ and 3², so must $N$ .

2² and 3 will be common to 84 and $N$ , with the additional prime factors of 2 and 3 belonging to $N$ alone.

$N = 2^{3} \times 3^{2} N = 8 \times 9 N = 72$

The prime factor of 7 must not be common to both (must belong to 84 alone), as 72 × 7 would result in a 3 digit answer.

$N = 72$ [1]

Prime Factors, HCF & LCM (Cambridge O Level Maths)

Exam Questions