Find the HCF and LCM of 12, 21 and 15

Video Explanation

Watch the video below for a clear explanation:

Solution

Question: The HCF and LCM of 12, 21 and 15 respectively are:

(a) 3, 140    (b) 12, 420    (c) 3, 420    (d) 420, 3

Step 1: Prime Factorisation

12 = 2² × 3

21 = 3 × 7

15 = 3 × 5

Step 2: Find the HCF

The HCF is the product of the common prime factors with the lowest powers.

Common prime factor = 3

∴ HCF = 3

Step 3: Find the LCM

The LCM is the product of the highest powers of all the prime factors present.

LCM = 2² × 3 × 5 × 7

LCM = 4 × 3 × 5 × 7

LCM = 420

Final Answer

✔ HCF = 3 and LCM = 420

✔ Correct option: (c) 3, 420

Conclusion

Thus, the HCF and LCM of 12, 21 and 15 are 3 and 420 respectively.