Next, we express 120 as a product of its prime factors. Dividing successively gives 120 = 2 × 2 × 2 × 3 × 5, which can be written in exponential form as 2³ × 3^1 × 5^1.

find the LCM of 72 and 120

Answer: $\text{LCM}(72, 120) = 360$

Step-by-step solution

Step 1: Prime factorisation of 72

We express $72$ as a product of its prime factors. Dividing successively by primes gives $72 = 2 \times 2 \times 2 \times 3 \times 3$ , which in exponential form is $2^3 \times 3^2$ .

Step 2: Prime factorisation of 120

Next, we express $120$ as a product of its prime factors. Dividing successively gives $120 = 2 \times 2 \times 2 \times 3 \times 5$ , which can be written in exponential form as $2^3 \times 3^1 \times 5^1$ .

Step 3: Find the LCM using the greatest powers

The LCM of two numbers is the product of the greatest power of each prime factor involved in the numbers. The prime factors involved are $2$ , $3$ , and $5$ . The greatest power of $2$ is $2^3$ , the greatest power of $3$ is $3^2$ , and the greatest power of $5$ is $5^1$ . Multiplying these gives $8 \times 9 \times 5 = 360$ .

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