Question

Three numbers are in the ratio of 2:3:4 and their LCM is 2400. Their HCF is?

1 point

150

100

120

200

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Answer 1

answer: 200

Step-by-step explanation:

when we do LCM of ratio after breaking ratio

is 12x.

12x=2400

x=200.

so,the numbers are - 400,600,800

HCF(400,600,800)=200

Answer 2

Answer:

Let the numbers be 2x, 3x and 4x respectively.

2x= 2 × x

3x= 3 × x

4x= 2 × 2 × x

∴ LCM(2x,3x,4x)= 2 × 2 × 3 × x= 12x

∴12x=2400

=>x=200

Thus, the nos. are 400, 600, 800

400= 2 × 2 × 2 × 2 × 5 × 5

600= 2 × 2 × 2 × 5 × 5 × 3

800= 2 × 2 × 2 × 2 × 2 × 5 × 5

∴HCF= 2 × 2 × 2 × 5 × 5= 200