Pythagorist
Numbers

LCM Calculator — Lowest Common Multiple

Find the lowest common multiple (LCM) of two numbers. The calculator uses the HCF-based method (LCM = a × b ÷ HCF) and shows every step of the working.

LCM(12, 18)

36

How it works

  1. First, find the HCF

    We use the relationship: LCM(a, b) = (a × b) ÷ HCF(a, b). So we first find HCF(12, 18).

  2. Apply the Euclidean algorithm

    The Euclidean algorithm: divide the larger number by the smaller, then repeat with (divisor, remainder) until the remainder is 0. The last non-zero remainder is the HCF.

  3. 18 = 12 × 1 + 6

    18=12×1+618 = 12 \times 1 + 6

    Remainder is 6. Now apply the algorithm to (12, 6).

  4. 12 = 6 × 2 + 0

    12=6×2+012 = 6 \times 2 + 0

    The remainder is 0, so the algorithm ends. The HCF is the last non-zero remainder (or divisor): 6.

    Result:HCF = 6

  5. Apply the LCM formula

    LCM(12,18)=12×18HCF(12,18)=2166=36\text{LCM}(12, 18) = \frac{12 \times 18}{\text{HCF}(12,18)} = \frac{216}{6} = 36

    LCM = (12 × 18) ÷ 6 = 216 ÷ 6 = 36.

    Result:36

The formula

LCM(a,b)=a×bHCF(a,b)\text{LCM}(a, b) = \frac{a \times b}{\text{HCF}(a, b)}
a,ba, bThe two numbers
HCF(a,b)HCF(a, b)The highest common factor of a and b

Example substitution

LCM(12,18)=12×186=2166=36\text{LCM}(12, 18) = \frac{12 \times 18}{6} = \frac{216}{6} = 36

HCF of 12 and 18 is 6. LCM = 12 × 18 ÷ 6 = 36.

Worked examples

Find the lowest common multiple of 4 and 6.

  1. 1
    Find HCF: HCF(4, 6) = 2
  2. 2
    Apply formula: 4 × 6 ÷ 2 = 12
Answer: 12

Find the lowest common multiple of 8 and 12.

  1. 1
    Find HCF: HCF(8, 12) = 4
  2. 2
    Apply formula: 8 × 12 ÷ 4 = 24
Answer: 24

Find the lowest common multiple of 15 and 25.

  1. 1
    Find HCF: HCF(15, 25) = 5
  2. 2
    Apply formula: 15 × 25 ÷ 5 = 75
Answer: 75

Frequently asked questions

What is the LCM?+

The lowest common multiple (LCM) is the smallest positive number that is a multiple of two or more given numbers.

How do you find the LCM?+

List multiples of each number until you find the first one they share. Or use the formula: LCM(a,b) = (a × b) / HCF(a,b).

What is the LCM of 4 and 6?+

Multiples of 4: 4, 8, 12, 16... Multiples of 6: 6, 12, 18... LCM = 12.

When do you need the LCM?+

The LCM is used when adding fractions (to find the common denominator), solving scheduling problems, and in number theory.

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