Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 153 and 159 the smallest integer that is 8109 that is divisible by both numbers.
Least Common Multiple (LCM) of 153 and 159 is 8109.
LCM(153,159) = 8109
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
Least common multiple can be found by multiplying the highest exponent prime factors of 153 and 159. First we will calculate the prime factors of 153 and 159.
Prime Factorization of 153
3 | 153 |
3 | 51 |
17 | 17 |
1 |
Prime factors of 153 are 3,17. Prime factorization of 153 in exponential form is:
153 = 32×171
Prime Factorization of 159
3 | 159 |
53 | 53 |
1 |
Prime factors of 159 are 3,53. Prime factorization of 159 in exponential form is:
159 = 31×531
Now multiplying the highest exponent prime factors to calculate the LCM of 153 and 159.
LCM(153,159) = 32×171×531
LCM(153,159) = 8109
Factors of 153
List of positive integer factors of 153 that divides 153 without a remainder.
1, 3, 9, 17, 51, 153
Factors of 159
List of positive integer factors of 159 that divides 159 without a remainder.
1, 3, 53, 159
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 153 and 159, than apply into the LCM equation.
GCF(153,159) = 3
LCM(153,159) = ( 153 × 159) / 3
LCM(153,159) = 24327 / 3
LCM(153,159) = 8109
(i) The LCM of 159 and 153 is associative
LCM of 153 and 159 = LCM of 159 and 153
1. What is the LCM of 153 and 159?
Answer: LCM of 153 and 159 is 8109.
2. What are the Factors of 153?
Answer: Factors of 153 are 1, 3, 9, 17, 51, 153. There are 6 integers that are factors of 153. The greatest factor of 153 is 153.
3. What are the Factors of 159?
Answer: Factors of 159 are 1, 3, 53, 159. There are 4 integers that are factors of 159. The greatest factor of 159 is 159.
4. How to Find the LCM of 153 and 159?
Answer:
Least Common Multiple of 153 and 159 = 8109
Step 1: Find the prime factorization of 153
153 = 3 x 3 x 17
Step 2: Find the prime factorization of 159
159 = 3 x 53
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 8109 = 3 x 3 x 17 x 53
Step 4: Therefore, the least common multiple of 153 and 159 is 8109.