Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 157 and 164 the smallest integer that is 25748 that is divisible by both numbers.
Least Common Multiple (LCM) of 157 and 164 is 25748.
LCM(157,164) = 25748
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 157 and 164. First we will calculate the prime factors of 157 and 164.
Prime Factorization of 157
157 | 157 |
1 |
Prime factors of 157 are 157. Prime factorization of 157 in exponential form is:
157 = 1571
Prime Factorization of 164
2 | 164 |
2 | 82 |
41 | 41 |
1 |
Prime factors of 164 are 2,41. Prime factorization of 164 in exponential form is:
164 = 22×411
Now multiplying the highest exponent prime factors to calculate the LCM of 157 and 164.
LCM(157,164) = 22×411×1571
LCM(157,164) = 25748
Factors of 157
List of positive integer factors of 157 that divides 157 without a remainder.
1, 157
Factors of 164
List of positive integer factors of 164 that divides 164 without a remainder.
1, 2, 4, 41, 82, 164
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 157 and 164, than apply into the LCM equation.
GCF(157,164) = 1
LCM(157,164) = ( 157 × 164) / 1
LCM(157,164) = 25748 / 1
LCM(157,164) = 25748
(i) The LCM of 164 and 157 is associative
LCM of 157 and 164 = LCM of 164 and 157
1. What is the LCM of 157 and 164?
Answer: LCM of 157 and 164 is 25748.
2. What are the Factors of 157?
Answer: Factors of 157 are 1, 157. There are 2 integers that are factors of 157. The greatest factor of 157 is 157.
3. What are the Factors of 164?
Answer: Factors of 164 are 1, 2, 4, 41, 82, 164. There are 6 integers that are factors of 164. The greatest factor of 164 is 164.
4. How to Find the LCM of 157 and 164?
Answer:
Least Common Multiple of 157 and 164 = 25748
Step 1: Find the prime factorization of 157
157 = 157
Step 2: Find the prime factorization of 164
164 = 2 x 2 x 41
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 25748 = 2 x 2 x 41 x 157
Step 4: Therefore, the least common multiple of 157 and 164 is 25748.