Least Common Multiple of 54 and 69
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 69 the smallest integer that is 1242 that is divisible by both numbers.
Least Common Multiple (LCM) of 54 and 69 is 1242.
LCM(54,69) = 1242
LCM of 54 and 69
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 54 and 69 by Prime method
- Least Common Multiple of 54 and 69 with GCF Formula
LCM of 54 and 69 is 1242
Least common multiple can be found by multiplying the highest exponent prime factors of 54 and 69. First we will calculate the prime factors of 54 and 69.
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 69
| 3 | 69 |
| 23 | 23 |
| 1 |
Prime factors of 69 are 3,23. Prime factorization of 69 in exponential form is:
69 = 31×231
Now multiplying the highest exponent prime factors to calculate the LCM of 54 and 69.
LCM(54,69) = 21×33×231
LCM(54,69) = 1242
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 69
List of positive integer factors of 69 that divides 69 without a remainder.
1, 3, 23, 69
Least Common Multiple of 54 and 69 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54 and 69, than apply into the LCM equation.
GCF(54,69) = 3
LCM(54,69) = ( 54 × 69) / 3
LCM(54,69) = 3726 / 3
LCM(54,69) = 1242
Properties of LCM 54 and 69
(i) The LCM of 69 and 54 is associative
LCM of 54 and 69 = LCM of 69 and 54
Related Least Common Multiples of 54
Related Least Common Multiples of 69
Frequently Asked Questions on LCM of 54 and 69
1. What is the LCM of 54 and 69?
Answer: LCM of 54 and 69 is 1242.
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 69?
Answer: Factors of 69 are 1, 3, 23, 69. There are 4 integers that are factors of 69. The greatest factor of 69 is 69.
4. How to Find the LCM of 54 and 69?
Answer:
Least Common Multiple of 54 and 69 = 1242
Step 1: Find the prime factorization of 54
54 = 2 x 3 x 3 x 3
Step 2: Find the prime factorization of 69
69 = 3 x 23
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1242 = 2 x 3 x 3 x 3 x 23
Step 4: Therefore, the least common multiple of 54 and 69 is 1242.
