To find Least Common Multiple by using Prime Factorization Method
To find least common multiple by using prime factorization method is discussed here.
To find the LCM of two or more numbers, we first find all the prime factors of the given numbers and write them one below the other. Take one factor from each common group of factors and find their product. Multiply the product with other ungrouped factors. The resultant is the LCM of given numbers.
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.
= 24 × 7 = 2 × 2 × 2 × 2 ×7 = 112.
Step III:
The required least common multiple (L.C.M) of 16 and 28 = 112.
3. Find the LCM of 32, 48 and 72 by prime factorization.
Solution:
LCM of 32, 48 and 72 = 2 × 2 × 2 × 2 × 2 × 3 × 3 = 288
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 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.
Recent Articles
-
Worksheet on Mixed Addition and Subtraction | Questions on Addition
Jan 12, 25 02:14 PM
In worksheet on mixed addition and subtraction the questions involve both addition and subtraction together; all grade students can practice the questions on addition and subtraction together. -
Estimating Sums and Differences | Estimations | Practical Calculations
Jan 12, 25 02:02 PM
For estimating sums and differences in the number we use the rounded numbers for estimations to its nearest tens, hundred, and thousand. In many practical calculations, only an approximation is requir… -
Combination of Addition and Subtraction | Mixed Addition & Subtraction
Jan 12, 25 01:36 PM
We will discuss here about the combination of addition and subtraction. The rules which can be used to solve the sums involving addition (+) and subtraction (-) together are: I: First add -
Checking Subtraction using Addition |Use Addition to Check Subtraction
Jan 12, 25 01:13 PM
We can check subtraction by adding the difference to the smaller number. Since the sum of difference and smaller number is equal to the larger number, subtraction is correct. -
Worksheet on Subtraction of 4-Digit Numbers|Subtracting 4-Digit Number
Jan 12, 25 09:04 AM
Practice the questions given in the worksheet on subtraction of 4-digit numbers. Here we will subtract two 4-digit numbers (without borrowing and with borrowing) to find the difference between them.
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.