Question

The ratio between the LCM and HCF of 5, 15, 20 is:

1 point

(a) 9 : 1

(b) 4:3

(c) 11:1

(d) 12:1

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Answer 1

Answer:

12:1 (LCM : HCM)

Step-by-step explanation:

5 = 5 * 1

15 = 5 * 3

20 = 5 * 4

so, 5 is common in all, so HCF is 5.

Now, you have to find a number which is divisible by 5,15 and 20.

Here, one thing is that if number is divisible by 15 then it is also divisible by 5 and if number is divisible by 20, then it is also divisible 5. So, you have to find LCM of 15 and 20.

15 = 5 * 3 and 20 = 5 * 4. HCF of this two is 5.

So, LCM = ( A * B ) / HCF ( A , B), in this formula put A = 15 and B = 20.

So, it is ( 15 * 20 ) / 5 = 60.

SO, HCF is 5 and LCM is 60. So, ratio of LCM and HCF is 12:1.

Answer 2

The correct option is d.

Given: The given numbers are 5, 15, 20.

To find The ratio between the LCM and HCF of 5, 15, 20.

Solution:

HCF is the highest common multiple of 5,15,20.

Thus the HCF of 5, 15, 20 will be-

$5 = 5 \times 1 \\ 15 = 5 \times 3 \\ 20 = 5 \times 4$

Thus the HCF is 5.

Now LCM is the lowest common multiple of 5, 15, 20.

So, LCM of 5, 15, 20 will be-

$5 = 5 \times 1 \\ 15 = 5 \times 3 \\ 20 = 5 \times 2 \times 2$

LCM is-

$5 \times 3 \times 2 \times 2 = 60$

Now the ratio between LCM and HCF of 5, 15, 20 is a ratio between 60 and 5.

$\frac{60}{5} = \frac{12}{1}$

Thus the ratio is 12:1.

The correct option is d.