A common multiple must contain enough prime factors to be divisible by each given integer. Take every prime occurring, to its greatest required power, to obtain the lowest common multiple (LCM). Example 18=2 x 32 and 24=23 x 3, so LCM(18,24)=23 x 32=72. Two signals flash together at 09:00, then every 18 and 24 minutes respectively. They next flash together 72 minutes later, at 10:12. Use HCF when dividing quantities into the greatest equal groups; use LCM when finding the first common total or recurrence. A common multiple is at least as large as each positive integer.

A common multiple must contain enough prime factors to be divisible by each given integer. Take every prime occurring, to its greatest required power, to obtain the lowest common multiple (LCM).

\(18=2\times3^2\) and \(24=2^3\times3\), so \(\operatorname{LCM}(18,24)=2^3\times3^2=72\).

Two signals flash together at 09:00, then every \(18\) and \(24\) minutes respectively. They next flash together \(72\) minutes later, at 10:12.

Use HCF when dividing quantities into the greatest equal groups; use LCM when finding the first common total or recurrence. A common multiple is at least as large as each positive integer.

Lowest common multiple

Lowest common multiple