6th Grade Greatest Common Factor and Least Common Multiple Quiz: 10 Questions with Explanations

A 5B 60C 10D 2

Common factors of 20 and 30 are 1, 2, 5, 10, and the greatest is 10. 60 is the LCM.

A 4B 96C 24D 48

Multiples of 12: 12, 24. 24 is also a multiple of 8. 4 is the GCF.

A \(2^{2} \times 3^{2}\)B \(2 \times 18\)C \(4 \times 9\)D \(2^{3} \times 3\)

\(36 = 2 \times 2 \times 3 \times 3\). The options \(2 \times 18\) and \(4 \times 9\) are not all prime factors.

A \(8(3 + 5)\)B \(4(6 + 10) + 8\)C \(8(3 + 40)\)D \(6(4 + 7)\)

\(8 \times 3 = 24\) and \(8 \times 5 = 40\), so 8(\(3 + 5\)).

A 6 and 9B 9 and 16C 8 and 12D 10 and 15

\(9 = 3 \times 3\) and \(16 = 2\)^4 share no prime factor.

A 5B 15C 30D 90

GCF of 30 and 45 is 15. 90 is the LCM.

A Every 3 secondsB Every 54 secondsC Every 15 secondsD Every 18 seconds

LCM of 6 and 9 is 18.

A 24B 12C 144D 6

\(48 = 2\)^\(4 \times 3\) and \(72 = 2\)^\(3 \times 3\)^2, so GCF = 2^\(3 \times 3 = 24\).

A 14B 60C 30D 45

60 is a multiple of 4 (\(4 \times 15\)) and of 10 (\(10 \times 6\)). 30 is not a multiple of 4.

A 7B 9C 56D 8

\(7 \times 8 = 56\).