1. Find the LCM of the following numbers by prime factorisation method. i. 12 and 15 ii. 15 and 25 iii. 14 and 21 iv. 18 and 27 v. 48, 56 and 72 vi. 26, 14 and 91. ( please answer fast )
Answers
Answer:
the lcm of 12 is
the lcm of 15 is
Answer:
1) LCM of 12 and 15 by Prime Factorization
Prime factorization of 12 and 15 is (2 × 2 × 3) = 22 × 31 and (3 × 5) = 31 × 51 respectively. LCM of 12 and 15 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 22 × 31 × 51 = 60. Hence, the LCM of 12 and 15 by prime factorization is 60.
2) LCM of 15 and 25 by Prime Factorization
Prime factorization of 15 and 25 is (3 × 5) = 31 × 51 and (5 × 5) = 52 respectively. LCM of 15 and 25 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 31 × 52 = 75. Hence, the LCM of 15 and 25 by prime factorization is 75.
3) LCM of 14 and 21 by Prime Factorization
Prime factorization of 14 and 21 is (2 × 7) = 21 × 71 and (3 × 7) = 31 × 71 respectively. LCM of 14 and 21 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 21 × 31 × 71 = 42. Hence, the LCM of 14 and 21 by prime factorization is 42.
4) LCM of 18 and 27 by Prime Factorization
Prime factorization of 18 and 27 is (2 × 3 × 3) = 21 × 32 and (3 × 3 × 3) = 33 respectively. LCM of 18 and 27 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 21 × 33 = 54. Hence, the LCM of 18 and 27 by prime factorization is 54.
5)LCM of 48, 56, and 72 by Prime Factorization
LCM of 48, 56, and 72 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 24 × 32 × 71 = 1008. Hence, the LCM of 48, 56, and 72 by prime factorization is 1008.
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