Examples to find least common multiple by using prime factorization method are discussed here.
We write the prime factorization of each of the given numbers. Then, the required LCM of these numbers is the product of all different prime factors of the numbers using the greatest power of each common prime factor.
1. What is the least common multiple (L.C.M) of 21 and 49 by using prime factorization method?
Solution:
To find the LCM, multiply all prime factors. But the common factors are included only once.
21 = 3 × 7.
49 = 7 × 7 = 7².
= 3 × 7² = 3 × 7 × 7 = 147.
The required least common multiple (L.C.M) of 21 and 49 = 98.
2. What is the least common multiple (L.C.M) of 36 and 14 by using prime factorization method?
Solution:
To find the LCM, multiply all prime factors. But the common factors are included only once.
36 = 2 × 2 × 3 × 3 = 2² × 3².
14 = 2 × 7.
= 2² × 3² × 7 = 2 × 2 × 3 × 3 × 7 = 252.
The required least common multiple (L.C.M) of 36 and 14 = 252.
3. What is the least common multiple (L.C.M) of 5, 4 and 16 by using prime factorization method?
Solution:
To find the LCM, multiply all prime factors. But the common factors are included only once.
5 = 5 × 1.
4 = 2 × 2.
16 = 2 × 2 × 2 × 2 = 2⁴.
= 2⁴ × 5 = 2 × 2 × 2 × 2 × 5 = 80.
The required least common multiple (L.C.M) of 5, 4 and 16 = 80.
4. Find L.C.M of 504 and 594 by prime factorization method.
Solution:
To find the LCM, multiply all prime factors. But the common factors are included only once.
504 = 2 × 2 × 2 × 3 × 3 × 7 = 2³ × 3³ × 7.
594 = 2 × 3 × 3 × 3 × 11 = 2 × 3³ × 11.
= 2³ × 3³ × 7 × 11 = 2 × 2 × 2 × 3 × 3 × 3 × 7 × 11 = 16632.
The required least common multiple (L.C.M) of 504 and 594 = 16632.
These are the four examples to find least common multiple by using prime factorization method.
Common Multiples.
Least Common Multiple (L.C.M).
To find Least Common Multiple by using Prime Factorization Method.
Examples to find Least Common Multiple by using Prime Factorization Method.
To Find Lowest Common Multiple by using Division Method
Examples to find Least Common Multiple of two numbers by using Division Method
Examples to find Least Common Multiple of three numbers by using Division Method
Relationship between H.C.F. and L.C.M.
Worksheet on H.C.F. and L.C.M.
Word problems on H.C.F. and L.C.M.
Worksheet on word problems on H.C.F. and L.C.M.
5th Grade Numbers Page
5th Grade Math Problems
From Examples to find Least Common Multiple by using Prime Factorization Method to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Aug 14, 24 09:52 AM
Aug 14, 24 02:39 AM
Aug 13, 24 01:27 AM
Aug 12, 24 03:20 PM
Aug 12, 24 02:23 AM
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.