Least Common Multiple of 63 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 63 and 75 the smallest integer that is 1575 that is divisible by both numbers.
Least Common Multiple (LCM) of 63 and 75 is 1575.
LCM(63,75) = 1575
LCM of 63 and 75
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 63 and 75 by Prime method
- Least Common Multiple of 63 and 75 with GCF Formula
LCM of 63 and 75 is 1575
Least common multiple can be found by multiplying the highest exponent prime factors of 63 and 75. First we will calculate the prime factors of 63 and 75.
Prime Factorization of 63
| 3 | 63 |
| 3 | 21 |
| 7 | 7 |
| 1 |
Prime factors of 63 are 3,7. Prime factorization of 63 in exponential form is:
63 = 32×71
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 63 and 75.
LCM(63,75) = 32×52×71
LCM(63,75) = 1575
Factors of 63
List of positive integer factors of 63 that divides 63 without a remainder.
1, 3, 7, 9, 21, 63
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 63 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 63 and 75, than apply into the LCM equation.
GCF(63,75) = 3
LCM(63,75) = ( 63 × 75) / 3
LCM(63,75) = 4725 / 3
LCM(63,75) = 1575
Properties of LCM 63 and 75
(i) The LCM of 75 and 63 is associative
LCM of 63 and 75 = LCM of 75 and 63
Related Least Common Multiples of 63
Related Least Common Multiples of 75
Frequently Asked Questions on LCM of 63 and 75
1. What is the LCM of 63 and 75?
Answer: LCM of 63 and 75 is 1575.
2. What are the Factors of 63?
Answer: Factors of 63 are 1, 3, 7, 9, 21, 63. There are 6 integers that are factors of 63. The greatest factor of 63 is 63.
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 63 and 75?
Answer:
Least Common Multiple of 63 and 75 = 1575
Step 1: Find the prime factorization of 63
63 = 3 x 3 x 7
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 = 1575 = 3 x 3 x 5 x 5 x 7
Step 4: Therefore, the least common multiple of 63 and 75 is 1575.
