Given that 168 = 2^3 × 3 × 7, find the lowest common multiple (LCM) of 168 and 30. - OCR - GCSE Maths - Question 2 - 2019 - Paper 1

Now, we will identify the highest powers of the prime factors from both numbers:

• For the prime number 2, the highest power is from 168, which is $2^3$.
• For the prime number 3, the highest power is $3^1$ (both 168 and 30 have $3^1$).
• For the prime number 5, the highest power is $5^1$ (only in 30).
• For the prime number 7, the highest power is $7^1$ (only in 168).

We can now calculate the LCM by multiplying the highest powers of all prime factors:

$LCM(168, 30) = 2^3 × 3^1 × 5^1 × 7^1$

Calculating this gives:

= 24 × 5 × 7 \\ = 120 × 7 \\ = 840$$ Thus, the lowest common multiple of 168 and 30 is 840.