Three numbers are in the ratio $2 : 3 : 4$ and their HCF is 12. What is their LCM?

48Correct answerYour answer72Correct answerYour answer144Correct answerYour answer288Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

The numbers are 24, 36 and 48.
$24 = 2^3 \times 3$ , $36 = 2^2 \times 3^2$ , $48 = 2^4 \times 3$ .
LCM = $2^4 \times 3^2 = 144$ .

Worth noting

288 comes from $12 \times 2 \times 3 \times 4$ , but 2 and 4 are not co-prime, so the shortcut HCF × (product of ratio terms) is wrong here. The correct multiplier is $\operatorname{LCM}(2, 3, 4) = 12$ .

Concept: Ratio and HCF with three numbers
Typical timeTypical: 60 s
Your timeYours: —

The rule this testsFinding HCF and LCM

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Ten questions from HCF & LCM, at your own pace.

Three numbers are in the ratio 2:3:42 : 3 : 42:3:4 and their HCF is 12. What is their LCM?

Explanation

Three numbers are in the ratio $2 : 3 : 4$ and their HCF is 12. What is their LCM?