Find Lowest Common Multiple (LCM) in Maths
Grade 7 Questions With Detailed Solutions

How do you find the lowest common multiple (LCM) of two or more numbers in maths? This page provides Grade 7 maths questions along with step-by-step solutions. Click the arrow below each question to reveal the detailed explanation.

What is the Lowest Common Multiple (LCM)?

It is the smallest whole number that is divisible by each of the given numbers. Alternatively, it is the smallest whole number that is a multiple of those numbers.

Two Methods to Find the LCM

Method 1: Listing Multiples (Best for small numbers)

Example: Find the LCM of 6 and 8.

List the first few multiples of both numbers and stop as soon as you find a common multiple.

The lowest common multiple of 6 and 8 is 24.

Method 2: Prime Factorization (Best for all numbers)

Example: Find the LCM of 42 and 60.

Step 1: Find the prime factorization of 42:
\( 42 = 2 \times 3 \times 7 \)

Step 2: Find the prime factorization of 60:
\( 60 = 2^2 \times 3 \times 5 \)

Step 3: The LCM is the product of all prime numbers found in the factorizations, using the highest power of each prime.

LCM = \( 2^2 \times 3^1 \times 5^1 \times 7^1 = 4 \times 3 \times 5 \times 7 = \mathbf{420} \)

Tip: You can use a Lowest Common Multiple Calculator to check your answers.

Practice Questions

  1. Question: Find the lowest common multiple of 5 and 15.
    View Step-by-Step Solution ▼

    The prime factorizations of 5 and 15 are:

    \( 5 = 5^1 \)

    \( 15 = 3^1 \times 5^1 \)

    The LCM is given by the product of all prime numbers in the factorization with the highest power:

    LCM = \( 3^1 \times 5^1 = \mathbf{15} \).

  2. Question: Find the lowest common multiple of 8, 12, and 18.
    View Step-by-Step Solution ▼

    Find the prime factorizations of 8, 12, and 18:

    \( 8 = 2 \times 2 \times 2 = 2^3 \)

    \( 12 = 2 \times 2 \times 3 = 2^2 \times 3^1 \)

    \( 18 = 2 \times 3 \times 3 = 2^1 \times 3^2 \)

    Take the highest power of each prime factor (2 and 3):

    LCM = \( 2^3 \times 3^2 = 8 \times 9 = \mathbf{72} \).

  3. Question: Find the lowest common multiple of 70 and 90.
    View Step-by-Step Solution ▼

    Find the prime factorizations of 70 and 90:

    \( 70 = 2^1 \times 5^1 \times 7^1 \)

    \( 90 = 2 \times 3 \times 3 \times 5 = 2^1 \times 3^2 \times 5^1 \)

    Take the highest power of each prime factor (2, 3, 5, and 7):

    LCM = \( 2^1 \times 3^2 \times 5^1 \times 7^1 = 2 \times 9 \times 5 \times 7 = \mathbf{630} \).

  4. Question: What is the lowest common multiple of 180, 216, and 450?
    View Step-by-Step Solution ▼

    Find the prime factorizations:

    \( 180 = 2 \times 2 \times 3 \times 3 \times 5 = 2^2 \times 3^2 \times 5^1 \)

    \( 216 = 2 \times 2 \times 2 \times 3 \times 3 \times 3 = 2^3 \times 3^3 \)

    \( 450 = 2 \times 3 \times 3 \times 5 \times 5 = 2^1 \times 3^2 \times 5^2 \)

    Take the highest power of each prime factor (2, 3, and 5):

    LCM = \( 2^3 \times 3^3 \times 5^2 = 8 \times 27 \times 25 = \mathbf{5400} \).

  5. Question: For the following pairs of numbers, find the LCM and the Greatest Common Factor (GCF). Then, compare the product of the LCM and GCF to the product of the original numbers.
    a) 12 and 16
    b) 30 and 45
    c) 60 and 160
    View Step-by-Step Solution ▼

    Part a) 12 and 16

    • Prime factorization: \( 12 = 2^2 \times 3 \),   \( 16 = 2^4 \)
    • GCF = \( 2^2 = 4 \)
    • LCM = \( 2^4 \times 3 = 48 \)
    • Product of LCM and GCF: \( 48 \times 4 = \mathbf{192} \)
    • Product of the numbers: \( 12 \times 16 = \mathbf{192} \)

    The two products are equal.

    Part b) 30 and 45

    • Prime factorization: \( 30 = 2 \times 3 \times 5 \),   \( 45 = 3^2 \times 5 \)
    • GCF = \( 3 \times 5 = 15 \)
    • LCM = \( 2 \times 3^2 \times 5 = 90 \)
    • Product of LCM and GCF: \( 90 \times 15 = \mathbf{1350} \)
    • Product of the numbers: \( 30 \times 45 = \mathbf{1350} \)

    The two products are equal.

    Part c) 60 and 160

    • Prime factorization: \( 60 = 2^2 \times 3 \times 5 \),   \( 160 = 2^5 \times 5 \)
    • GCF = \( 2^2 \times 5 = 20 \)
    • LCM = \( 2^5 \times 3 \times 5 = 480 \)
    • Product of LCM and GCF: \( 480 \times 20 = \mathbf{9600} \)
    • Product of the numbers: \( 60 \times 160 = \mathbf{9600} \)

    The two products are equal.

    Conclusion: It is always true that for any two whole numbers \( M \) and \( N \), the relationship is:
    \( \text{GCF} \times \text{LCM} = M \times N \)

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