Least Common Multiple of 52 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 52 and 69 the smallest integer that is 3588 that is divisible by both numbers.
Least Common Multiple (LCM) of 52 and 69 is 3588.
LCM(52,69) = 3588
LCM of 52 and 69
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 52 and 69 by Prime method
- Least Common Multiple of 52 and 69 with GCF Formula
LCM of 52 and 69 is 3588
Least common multiple can be found by multiplying the highest exponent prime factors of 52 and 69. First we will calculate the prime factors of 52 and 69.
Prime Factorization of 52
| 2 | 52 |
| 2 | 26 |
| 13 | 13 |
| 1 |
Prime factors of 52 are 2,13. Prime factorization of 52 in exponential form is:
52 = 22×131
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 52 and 69.
LCM(52,69) = 22×31×131×231
LCM(52,69) = 3588
Factors of 52
List of positive integer factors of 52 that divides 52 without a remainder.
1, 2, 4, 13, 26, 52
Factors of 69
List of positive integer factors of 69 that divides 69 without a remainder.
1, 3, 23, 69
Least Common Multiple of 52 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 52 and 69, than apply into the LCM equation.
GCF(52,69) = 1
LCM(52,69) = ( 52 × 69) / 1
LCM(52,69) = 3588 / 1
LCM(52,69) = 3588
Properties of LCM 52 and 69
(i) The LCM of 69 and 52 is associative
LCM of 52 and 69 = LCM of 69 and 52
Related Least Common Multiples of 52
Related Least Common Multiples of 69
Frequently Asked Questions on LCM of 52 and 69
1. What is the LCM of 52 and 69?
Answer: LCM of 52 and 69 is 3588.
2. What are the Factors of 52?
Answer: Factors of 52 are 1, 2, 4, 13, 26, 52. There are 6 integers that are factors of 52. The greatest factor of 52 is 52.
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 52 and 69?
Answer:
Least Common Multiple of 52 and 69 = 3588
Step 1: Find the prime factorization of 52
52 = 2 x 2 x 13
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 = 3588 = 2 x 2 x 3 x 13 x 23
Step 4: Therefore, the least common multiple of 52 and 69 is 3588.
