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10 grade maths

Find the least common multiple of 9, 36, 45?

Profile image of Aniket Singh
1 Year agoGrade
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1 Answer

Profile image of Askiitians Tutor Team
1 Year ago

To find the least common multiple (LCM) of 9, 36, and 45, follow these steps:

Find the prime factorization of each number:

9: The prime factorization of 9 is 9 = 3 × 3 = 3².
36: The prime factorization of 36 is 36 = 2 × 2 × 3 × 3 = 2² × 3².
45: The prime factorization of 45 is 45 = 3 × 3 × 5 = 3² × 5.
Identify the highest power of each prime factor:

For 2, the highest power is 2² (from 36).
For 3, the highest power is 3² (appears in all three numbers).
For 5, the highest power is 5 (from 45).
Multiply the highest powers of all the primes:

LCM = 2² × 3² × 5 = 4 × 9 × 5 = 180.

So, the least common multiple of 9, 36, and 45 is 180.

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