Question

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

Explain your answer.
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Answer 1

Answer:

Option (c) 1:12 is the correct answer.

Step-by-step explanation:

The prime factors of 15, 20 and 5 are:-

15 = 3×5

20 = 2²×5

and 5 = 5

So, HCF of ( 15, 20, 5 ) = 5

LCM of ( 15, 20, 5 ) = 2² × 3 × 5 = 60

Therefore,

Required ratio = HCF / LCM

= 5/60

= 1/12 or 1:12

hope it helps you.

Answer 2

$\large\underline{\sf{Solution-}}$

Given numbers are 15, 20 and 5

Let's first evaluate the prime factors of 15, 20 and 5

Consider,

$\rm \: Prime\:factorization\:of\:15$

$\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{3}}}&{\underline{\sf{\:\:15 \:\:}}}\\ {\underline{\sf{5}}}& \underline{\sf{\:\:5 \:\:}} \\\underline{\sf{}}&{\sf{\:\:1 \:\:}} \end{array}\end{gathered}\end{gathered}\end{gathered}$

$\rm \: Prime\:factorization\:of\:15 = 3 \times 5$

Now, Consider

$\rm \: Prime\:factorization\:of\:20$

$\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{2}}}&{\underline{\sf{\:\:20 \:\:}}}\\ {\underline{\sf{2}}}& \underline{\sf{\:\:10 \:\:}} \\ {\underline{\sf{5}}}& \underline{\sf{\:\:5\:\:}}\\\underline{\sf{}}&{\sf{\:\:1 \:\:}} \end{array}\end{gathered}\end{gathered}\end{gathered}$

$\rm \: Prime\:factorization\:of\:20 = 2 \times 2 \times 5$

Also,

$\rm \: Prime\:factorization\:of\:5 = 5$

So, we have

$\rm \: Prime\:factorization\:of\:5 = 5$

$\rm \: Prime\:factorization\:of\:15 = 3 \times 5$

$\rm \: Prime\:factorization\:of\:20 = 2 \times 2 \times 5$

So,

$\rm\implies \:HCF(5,15,20) = 5$

$\rm\implies \:LCM(5,15,20) = 2 \times 2 \times 3 \times 5 = 60$

Hence,

$\rm \: HCF : LCM$

$\rm \: = \: 5 : 60$

$\rm \: = \: 1 : 12$

So, option (c) is correct.

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ADDITIONAL INFORMATION

If a and b are two natural numbers, then

• HCF (a, b) × LCM (a, b) = a × b

• LCM is always divisible by a, b and HCF

• HCF always divides a, b and LCM

If a and b are two co prime natural numbers, then

• HCF (a, b) = 1

• LCM (a, b) = ab

Smallest prime number is 2

Smallest Composite number is 4

Smallest odd composite number is 9