How do you get the least common multiple of 18 27 and 35?

Answer 1

The prime factorization of their least common multiple will contain their prime factorizations.

2 x 3 x 3 = 18

3 x 3 x 3 = 27

5 x 7 = 35

The LCM needs to have a two, three threes, a five and a seven.

2 x 3 x 3 x 3 x 5 x 7 = 1890, the LCM

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For an algorithm to follow:

1. Prime factorize the numbers using power format
2. multiply together the primes with their highest power.

18 = 2 × 3²

27 = 3³

35 = 5 × 7

Highest power of 2 is 2

Highest power of 3 is 3³

Highest power of 5 is 5

Highest power of 7 is 7

→ lcm(18, 27, 35) = 2 × 3³ × 5 × 7 = 1890

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Their hcf can be found with a similar algorithm:

1. Prime factorize the numbers using power format
2. multiply together the primes common to all the numbers with their lowest power.
3. If there are no primes common to all the numbers, the hcf is 1.

For 18, 27 and 35 there are no primes common to all three numbers so hcf(18, 27, 35) = 1

Considering only 18 and 27, the common primes consists of only 3 which has the lowest power of 3² (from the prime factorization of 18) → hcf(18, 27) = 3³ = 9.

Answer 2

LCM(1827, 35) = 9135