Question

19.The ratio between the LCM and HCF of 5, 15, 20 is:
(a) 9 : 1 (b) 4 : 3 (c) 11 : 1 (d) 12 : 1​

Answer 1

Required Answer:-

• LCM is the lowest common multiple which is the smallest number evenly divisible by two numbers.

• And HCF is the highest common factor which is the largest number which evenly divides the other too$.$

Finding LCM and HCF by prime factorisation:

5 = 5¹

15 = 3¹ × 5¹

20 = 2² × 5¹

Now here LCM will be the product of prime factors in their highest degree in all three numbers. And HCF will be the product of lowest degree of prime factors common to them.

Then,

LCM of 5, 15 and 20 = 5¹ × 3¹ × 2² = 60

HCF of 5, 15 and 20 = 5¹ = 5

Hence:

• Required ratio of LCM and HCF of 5, 15 and 20 is 60 : 5 i.e. 12 : 1 (Option D).

Answer 2

Answer:

Given :-

Ratio between LCM and HCF of 5,15,20

To Find :-

The ratio

Solution :-

For finding ratio we will first find the LCM and HCF of 5,15,20

$\tt \: LCM \: (lowest \: common \: multiple)$

$\tt \: 5 = 5$

$\tt \: 15 = 3 \times 5$

$\tt \: 20 = 2 \: \times 2 \times 5$

LCM = 5 × 2 × 2 × 3 = 60

$\tt \: HCF \: (highest \: common \: factor)$

$\tt \: factor \: of \: 5 = 1 \: and \: 5$

$\tt \: factor \: of \: 15 \: = 1, \: 3, \: 5 \: and \:15$

$\tt \: fator \: of \: 20 = 1,\: 2,\: 4,\: 5,\: 10, \: and \: 20$

Common Multiple = 5 only

Therefore

HCF = 5 and LCM = 60

Ratio = 60/5 = 12/1 = 12:1

(Option D)