Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 54 and 72 the smallest integer that is 216 that is divisible by both numbers.
Least Common Multiple (LCM) of 54 and 72 is 216.
LCM(54,72) = 216
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 54 and 72. First we will calculate the prime factors of 54 and 72.
Prime Factorization of 54
2 | 54 |
3 | 27 |
3 | 9 |
3 | 3 |
1 |
Prime factors of 54 are 2,3. Prime factorization of 54 in exponential form is:
54 = 21×33
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
Now multiplying the highest exponent prime factors to calculate the LCM of 54 and 72.
LCM(54,72) = 23×33
LCM(54,72) = 216
Factors of 54
List of positive integer factors of 54 that divides 54 without a remainder.
1, 2, 3, 6, 9, 18, 27, 54
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
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54 and 72, than apply into the LCM equation.
GCF(54,72) = 18
LCM(54,72) = ( 54 × 72) / 18
LCM(54,72) = 3888 / 18
LCM(54,72) = 216
(i) The LCM of 72 and 54 is associative
LCM of 54 and 72 = LCM of 72 and 54
1. What is the LCM of 54 and 72?
Answer: LCM of 54 and 72 is 216.
2. What are the Factors of 54?
Answer: Factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54. There are 8 integers that are factors of 54. The greatest factor of 54 is 54.
3. 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.
4. How to Find the LCM of 54 and 72?
Answer:
Least Common Multiple of 54 and 72 = 216
Step 1: Find the prime factorization of 54
54 = 2 x 3 x 3 x 3
Step 2: Find the prime factorization of 72
72 = 2 x 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 = 216 = 2 x 2 x 2 x 3 x 3 x 3
Step 4: Therefore, the least common multiple of 54 and 72 is 216.