Question

Three numbers are in the ratio of 2 : 3 : 5 and their l.c.m. is 1800 their h.c.f. is​

Answer 1

Let the nos. be 2x, 3x nd 5x

Then, their lcm be 30x

So, 30x = 1800

x= 60

Now, nos. are (2*75) (3*75) (5*75)

Hence, required HCF = 75

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Answer 2

HCF : Number which greatest or highest factor of all the given terms, It is called Highest Common Factor. It is always less than all the given terms.

LCM : Number which smallest or lowest multiple of all the given terms, It is called Least Common Multiple. It is always more than all the given terms.

Here is a thing to understand before solving this question. LCM consists of HCF and all the number left after it.

• According to the Question :

⇒ (1st × 2nd × 3rd)No. × HCF = LCM

⇒ (2 × 3 × 5) × HCF = 1800

⇒ 30 × HCF = 1800

⇒ HCF = 1800 ÷ 30

⇒ HCF = 60

∴ Hence, HCF of three numbers is 60.

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Verification –

• 1st Number = 2 × HCF = 2 × 60 = 120
• 2nd Number = 3 × HCF = 3 × 60 = 180
• 3rd Number = 5 × HCF = 5 × 60 = 300

⇢ HCF = Common Factor = 60

⇢ LCM = Common Multiple = 2 × 3 × 5 × 60 = 1800