Least Common Multiple of 69 and 72
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 69 and 72 the smallest integer that is 1656 that is divisible by both numbers.
Least Common Multiple (LCM) of 69 and 72 is 1656.
LCM(69,72) = 1656
LCM of 69 and 72
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 69 and 72 by Prime method
- Least Common Multiple of 69 and 72 with GCF Formula
LCM of 69 and 72 is 1656
Least common multiple can be found by multiplying the highest exponent prime factors of 69 and 72. First we will calculate the prime factors of 69 and 72.
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
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 69 and 72.
LCM(69,72) = 23×32×231
LCM(69,72) = 1656
Factors of 69
List of positive integer factors of 69 that divides 69 without a remainder.
1, 3, 23, 69
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
Least Common Multiple of 69 and 72 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 69 and 72, than apply into the LCM equation.
GCF(69,72) = 3
LCM(69,72) = ( 69 × 72) / 3
LCM(69,72) = 4968 / 3
LCM(69,72) = 1656
Properties of LCM 69 and 72
(i) The LCM of 72 and 69 is associative
LCM of 69 and 72 = LCM of 72 and 69
Related Least Common Multiples of 69
Related Least Common Multiples of 72
Frequently Asked Questions on LCM of 69 and 72
1. What is the LCM of 69 and 72?
Answer: LCM of 69 and 72 is 1656.
2. 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.
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 69 and 72?
Answer:
Least Common Multiple of 69 and 72 = 1656
Step 1: Find the prime factorization of 69
69 = 3 x 23
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 = 1656 = 2 x 2 x 2 x 3 x 3 x 23
Step 4: Therefore, the least common multiple of 69 and 72 is 1656.