1. (a) Write 84 as a product of its prime factors - Edexcel - GCSE Maths - Question 3 - 2020 - Paper 2

To find the LCM of 60 and 84, we first determine their prime factorizations:

• The prime factorization of 60 is:

  $60 = 2^2 \times 3^1 \times 5^1$

• The prime factorization of 84 (as found earlier) is:

  $84 = 2^2 \times 3^1 \times 7^1$

Next, we find the LCM by taking the highest power of each prime number from both factorizations:

• For 2: maximum power is $2^2$
• For 3: maximum power is $3^1$
• For 5: maximum power is $5^1$
• For 7: maximum power is $7^1$

Thus, the LCM is:

$LCM(60, 84) = 2^2 \times 3^1 \times 5^1 \times 7^1$

Calculating this gives:

$LCM(60, 84) = 4 \times 3 \times 5 \times 7 = 420$