Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 25 and 60 the smallest integer that is 300 that is divisible by both numbers.
Least Common Multiple (LCM) of 25 and 60 is 300.
LCM(25,60) = 300
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 25 and 60. First we will calculate the prime factors of 25 and 60.
Prime Factorization of 25
5 | 25 |
5 | 5 |
1 |
Prime factors of 25 are 5. Prime factorization of 25 in exponential form is:
25 = 52
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 25 and 60.
LCM(25,60) = 22×31×52
LCM(25,60) = 300
Factors of 25
List of positive integer factors of 25 that divides 25 without a remainder.
1, 5, 25
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 25 and 60, than apply into the LCM equation.
GCF(25,60) = 5
LCM(25,60) = ( 25 × 60) / 5
LCM(25,60) = 1500 / 5
LCM(25,60) = 300
(i) The LCM of 60 and 25 is associative
LCM of 25 and 60 = LCM of 60 and 25
1. What is the LCM of 25 and 60?
Answer: LCM of 25 and 60 is 300.
2. What are the Factors of 25?
Answer: Factors of 25 are 1, 5, 25. There are 3 integers that are factors of 25. The greatest factor of 25 is 25.
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 25 and 60?
Answer:
Least Common Multiple of 25 and 60 = 300
Step 1: Find the prime factorization of 25
25 = 5 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 = 300 = 2 x 2 x 3 x 5 x 5
Step 4: Therefore, the least common multiple of 25 and 60 is 300.