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 36 the smallest integer that is 900 that is divisible by both numbers.
Least Common Multiple (LCM) of 25 and 36 is 900.
LCM(25,36) = 900
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 36. First we will calculate the prime factors of 25 and 36.
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 36
2 | 36 |
2 | 18 |
3 | 9 |
3 | 3 |
1 |
Prime factors of 36 are 2,3. Prime factorization of 36 in exponential form is:
36 = 22×32
Now multiplying the highest exponent prime factors to calculate the LCM of 25 and 36.
LCM(25,36) = 22×32×52
LCM(25,36) = 900
Factors of 25
List of positive integer factors of 25 that divides 25 without a remainder.
1, 5, 25
Factors of 36
List of positive integer factors of 36 that divides 36 without a remainder.
1, 2, 3, 4, 6, 9, 12, 18, 36
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 25 and 36, than apply into the LCM equation.
GCF(25,36) = 1
LCM(25,36) = ( 25 × 36) / 1
LCM(25,36) = 900 / 1
LCM(25,36) = 900
(i) The LCM of 36 and 25 is associative
LCM of 25 and 36 = LCM of 36 and 25
1. What is the LCM of 25 and 36?
Answer: LCM of 25 and 36 is 900.
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 36?
Answer: Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. There are 9 integers that are factors of 36. The greatest factor of 36 is 36.
4. How to Find the LCM of 25 and 36?
Answer:
Least Common Multiple of 25 and 36 = 900
Step 1: Find the prime factorization of 25
25 = 5 x 5
Step 2: Find the prime factorization of 36
36 = 2 x 2 x 3 x 3
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 900 = 2 x 2 x 3 x 3 x 5 x 5
Step 4: Therefore, the least common multiple of 25 and 36 is 900.