Least Common Multiple of 69 and 75
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 75 the smallest integer that is 1725 that is divisible by both numbers.
Least Common Multiple (LCM) of 69 and 75 is 1725.
LCM(69,75) = 1725
LCM of 69 and 75
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 69 and 75 by Prime method
- Least Common Multiple of 69 and 75 with GCF Formula
LCM of 69 and 75 is 1725
Least common multiple can be found by multiplying the highest exponent prime factors of 69 and 75. First we will calculate the prime factors of 69 and 75.
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 75
| 3 | 75 |
| 5 | 25 |
| 5 | 5 |
| 1 |
Prime factors of 75 are 3,5. Prime factorization of 75 in exponential form is:
75 = 31×52
Now multiplying the highest exponent prime factors to calculate the LCM of 69 and 75.
LCM(69,75) = 31×52×231
LCM(69,75) = 1725
Factors of 69
List of positive integer factors of 69 that divides 69 without a remainder.
1, 3, 23, 69
Factors of 75
List of positive integer factors of 75 that divides 75 without a remainder.
1, 3, 5, 15, 25, 75
Least Common Multiple of 69 and 75 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 75, than apply into the LCM equation.
GCF(69,75) = 3
LCM(69,75) = ( 69 × 75) / 3
LCM(69,75) = 5175 / 3
LCM(69,75) = 1725
Properties of LCM 69 and 75
(i) The LCM of 75 and 69 is associative
LCM of 69 and 75 = LCM of 75 and 69
Related Least Common Multiples of 69
Related Least Common Multiples of 75
Frequently Asked Questions on LCM of 69 and 75
1. What is the LCM of 69 and 75?
Answer: LCM of 69 and 75 is 1725.
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 75?
Answer: Factors of 75 are 1, 3, 5, 15, 25, 75. There are 6 integers that are factors of 75. The greatest factor of 75 is 75.
4. How to Find the LCM of 69 and 75?
Answer:
Least Common Multiple of 69 and 75 = 1725
Step 1: Find the prime factorization of 69
69 = 3 x 23
Step 2: Find the prime factorization of 75
75 = 3 x 5 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 = 1725 = 3 x 5 x 5 x 23
Step 4: Therefore, the least common multiple of 69 and 75 is 1725.
