Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 45 and 60 the smallest integer that is 180 that is divisible by both numbers.
Least Common Multiple (LCM) of 45 and 60 is 180.
LCM(45,60) = 180
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 45 and 60. First we will calculate the prime factors of 45 and 60.
Prime Factorization of 45
3 | 45 |
3 | 15 |
5 | 5 |
1 |
Prime factors of 45 are 3,5. Prime factorization of 45 in exponential form is:
45 = 32×51
Prime Factorization of 60
2 | 60 |
2 | 30 |
3 | 15 |
5 | 5 |
1 |
Prime factors of 60 are 2, 3,5. Prime factorization of 60 in exponential form is:
60 = 22×31×51
Now multiplying the highest exponent prime factors to calculate the LCM of 45 and 60.
LCM(45,60) = 22×32×51
LCM(45,60) = 180
Factors of 45
List of positive integer factors of 45 that divides 45 without a remainder.
1, 3, 5, 9, 15, 45
Factors of 60
List of positive integer factors of 60 that divides 60 without a remainder.
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 45 and 60, than apply into the LCM equation.
GCF(45,60) = 15
LCM(45,60) = ( 45 × 60) / 15
LCM(45,60) = 2700 / 15
LCM(45,60) = 180
(i) The LCM of 60 and 45 is associative
LCM of 45 and 60 = LCM of 60 and 45
1. What is the LCM of 45 and 60?
Answer: LCM of 45 and 60 is 180.
2. What are the Factors of 45?
Answer: Factors of 45 are 1, 3, 5, 9, 15, 45. There are 6 integers that are factors of 45. The greatest factor of 45 is 45.
3. What are the Factors of 60?
Answer: Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. There are 12 integers that are factors of 60. The greatest factor of 60 is 60.
4. How to Find the LCM of 45 and 60?
Answer:
Least Common Multiple of 45 and 60 = 180
Step 1: Find the prime factorization of 45
45 = 3 x 3 x 5
Step 2: Find the prime factorization of 60
60 = 2 x 2 x 3 x 5
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 180 = 2 x 2 x 3 x 3 x 5
Step 4: Therefore, the least common multiple of 45 and 60 is 180.