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What are the two smallest numbers whose gcf is 9 and whose LCM is 54?
Wiki User
∙ 8y ago
The two numbers 18 and 27.
Factorising the lcm and gcf gives:
54 = 2 × 3³
9 = 3²
There must be 3² in both numbers, but there must be a 3³ and a 2 which must appear in the prime factorisations of the two numbers. Putting a 2 with one 3² and a 3 with the other 3² leads to the two numbers:
2 × 3² = 18
3 × 3³ = 3³ = 27
as the two smallest numbers with gcf=9 and lcm=54. The other distribution of both 2 and 3 with one 3² results in the two number 3² = 9 and 2 × 3³ = 54, the latter of which is larger than both the 18 and 27 previously found.
Wiki User
∙ 8y ago
Wiki User
∙ 11y ago18 and 27
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