Least Common Multiple of 75 and 3
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 75 and 3 the smallest integer that is 75 that is divisible by both numbers.
Least Common Multiple (LCM) of 75 and 3 is 75.
LCM(75,3) = 75
LCM of 75 and 3
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 75 and 3 by Prime method
- Least Common Multiple of 75 and 3 with GCF Formula
LCM of 75 and 3 is 75
Least common multiple can be found by multiplying the highest exponent prime factors of 75 and 3. First we will calculate the prime factors of 75 and 3.
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
Prime Factorization of 3
| 3 | 3 |
| 1 |
Prime factors of 3 are 3. Prime factorization of 3 in exponential form is:
3 = 31
Now multiplying the highest exponent prime factors to calculate the LCM of 75 and 3.
LCM(75,3) = 31×52
LCM(75,3) = 75
Factors of 75
List of positive integer factors of 75 that divides 75 without a remainder.
1, 3, 5, 15, 25, 75
Factors of 3
List of positive integer factors of 3 that divides 3 without a remainder.
1, 3
Least Common Multiple of 75 and 3 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75 and 3, than apply into the LCM equation.
GCF(75,3) = 3
LCM(75,3) = ( 75 × 3) / 3
LCM(75,3) = 225 / 3
LCM(75,3) = 75
Properties of LCM 75 and 3
(i) The LCM of 3 and 75 is associative
LCM of 75 and 3 = LCM of 3 and 75
Related Least Common Multiples of 75
Related Least Common Multiples of 3
Frequently Asked Questions on LCM of 75 and 3
1. What is the LCM of 75 and 3?
Answer: LCM of 75 and 3 is 75.
2. 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.
3. What are the Factors of 3?
Answer: Factors of 3 are 1, 3. There are 2 integers that are factors of 3. The greatest factor of 3 is 3.
4. How to Find the LCM of 75 and 3?
Answer:
Least Common Multiple of 75 and 3 = 75
Step 1: Find the prime factorization of 75
75 = 3 x 5 x 5
Step 2: Find the prime factorization of 3
3 = 3
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 75 = 3 x 5 x 5
Step 4: Therefore, the least common multiple of 75 and 3 is 75.
