find the lcm by short division 105,126,147
Answers
Step-by-step explanation:
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To find Least Common Multiple by using Prime Factorization Method
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To find least common multiple by using prime factorization method is discussed here.
Step I:
Resolve each given number into its prime factors and express the factors obtained in exponent form.
Step I:
Find the product of the highest powers of all the factors that occur in any of the given numbers.
Step III:
The product obtained in Step II is the required least common multiple (L.C.M).
For example:
1. Find the least common multiple (L.C.M) of 9 and 15 by using prime factorization method.
Solution:
Step I:
Resolving each given number into its prime factors.
9 = 3 × 3 = 3².
15 = 3 × 5.
Step II:
The product of all the factors with highest powers.
= 3^2 × 5 = 3 × 3 × 5 = 45.
Step III:
The required least common multiple (L.C.M) of 9 and 15 = 45.
2. What is the least common multiple (L.C.M) of 16 and 28 by using prime factorization method?
Solution:
Step I:
Resolving each given number into its prime factors.
16 = 2 × 2 × 2 × 2 = 2⁴.
28 = 2 × 2 × 7 = 2² × 7.
Step II:
The product of all the factors with highest powers.
= 2^4 × 7 = 2 × 2 × 2 × 2 ×7 = 112.
Step III:
The required least common multiple (L.C.M) of 16 and 28 = 112.