The Ministry is migrating nzmaths content to Tāhurangi.
Relevant and up-to-date teaching resources are being moved to Tāhūrangi (tahurangi.education.govt.nz).
When all identified resources have been successfully moved, this website will close. We expect this to be in June 2024.
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For more information visit https://tahurangi.education.govt.nz/updates-to-nzmaths
An integer a is a common multiple of two integers b and c if it is a multiple of both b and c. For example, the multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, …The multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, …The common multiples of 4 and 6 are therefore the numbers 12, 24, 36, 48, …Unlike a set of common factors, this is an infinite set, the set of multiples of 12. The primenumber factorisations of 4 and 6 are 2 x 2 and 2 x 3 respectively. So the common multiples of 4 and 6 are multiples of 2 x 2 x 3, which equals 12.
So the least common multiple (often abbreviated to l.c.m.) of 4 and 6 is 12. The least common multiple of any two integers can also be found as the product of the numbers divided by their greatest common factor, that is, for integers a and b, l.c.m. of a and b = (a x b)÷(g.c.f. of a and b) In the example above, the l.c.m. of 6 and 4 = (6 x 4)÷2 = 12.
