Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 12 and 25 the smallest integer that is 300 that is divisible by both numbers.
Least Common Multiple (LCM) of 12 and 25 is 300.
LCM(12,25) = 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 12 and 25. First we will calculate the prime factors of 12 and 25.
Prime Factorization of 12
2 | 12 |
2 | 6 |
3 | 3 |
1 |
Prime factors of 12 are 2,3. Prime factorization of 12 in exponential form is:
12 = 22×31
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
Now multiplying the highest exponent prime factors to calculate the LCM of 12 and 25.
LCM(12,25) = 22×31×52
LCM(12,25) = 300
Factors of 12
List of positive integer factors of 12 that divides 12 without a remainder.
1, 2, 3, 4, 6, 12
Factors of 25
List of positive integer factors of 25 that divides 25 without a remainder.
1, 5, 25
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12 and 25, than apply into the LCM equation.
GCF(12,25) = 1
LCM(12,25) = ( 12 × 25) / 1
LCM(12,25) = 300 / 1
LCM(12,25) = 300
(i) The LCM of 25 and 12 is associative
LCM of 12 and 25 = LCM of 25 and 12
1. What is the LCM of 12 and 25?
Answer: LCM of 12 and 25 is 300.
2. What are the Factors of 12?
Answer: Factors of 12 are 1, 2, 3, 4, 6, 12. There are 6 integers that are factors of 12. The greatest factor of 12 is 12.
3. 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.
4. How to Find the LCM of 12 and 25?
Answer:
Least Common Multiple of 12 and 25 = 300
Step 1: Find the prime factorization of 12
12 = 2 x 2 x 3
Step 2: Find the prime factorization of 25
25 = 5 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 12 and 25 is 300.