Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 72 and 90 the smallest integer that is 360 that is divisible by both numbers.
Least Common Multiple (LCM) of 72 and 90 is 360.
LCM(72,90) = 360
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 72 and 90. First we will calculate the prime factors of 72 and 90.
Prime Factorization of 72
2 | 72 |
2 | 36 |
2 | 18 |
3 | 9 |
3 | 3 |
1 |
Prime factors of 72 are 2,3. Prime factorization of 72 in exponential form is:
72 = 23×32
Prime Factorization of 90
2 | 90 |
3 | 45 |
3 | 15 |
5 | 5 |
1 |
Prime factors of 90 are 2, 3,5. Prime factorization of 90 in exponential form is:
90 = 21×32×51
Now multiplying the highest exponent prime factors to calculate the LCM of 72 and 90.
LCM(72,90) = 23×32×51
LCM(72,90) = 360
Factors of 72
List of positive integer factors of 72 that divides 72 without a remainder.
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Factors of 90
List of positive integer factors of 90 that divides 90 without a remainder.
1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 72 and 90, than apply into the LCM equation.
GCF(72,90) = 18
LCM(72,90) = ( 72 × 90) / 18
LCM(72,90) = 6480 / 18
LCM(72,90) = 360
(i) The LCM of 90 and 72 is associative
LCM of 72 and 90 = LCM of 90 and 72
1. What is the LCM of 72 and 90?
Answer: LCM of 72 and 90 is 360.
2. What are the Factors of 72?
Answer: Factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72. There are 12 integers that are factors of 72. The greatest factor of 72 is 72.
3. What are the Factors of 90?
Answer: Factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90. There are 12 integers that are factors of 90. The greatest factor of 90 is 90.
4. How to Find the LCM of 72 and 90?
Answer:
Least Common Multiple of 72 and 90 = 360
Step 1: Find the prime factorization of 72
72 = 2 x 2 x 2 x 3 x 3
Step 2: Find the prime factorization of 90
90 = 2 x 3 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 = 360 = 2 x 2 x 2 x 3 x 3 x 5
Step 4: Therefore, the least common multiple of 72 and 90 is 360.