Least Common Multiple of 54 and 63
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 54 and 63 the smallest integer that is 378 that is divisible by both numbers.
Least Common Multiple (LCM) of 54 and 63 is 378.
LCM(54,63) = 378
LCM of 54 and 63
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
- Least Common Multiple of 54 and 63 by Prime method
- Least Common Multiple of 54 and 63 with GCF Formula
LCM of 54 and 63 is 378
Least common multiple can be found by multiplying the highest exponent prime factors of 54 and 63. First we will calculate the prime factors of 54 and 63.
Prime Factorization of 54
| 2 | 54 |
| 3 | 27 |
| 3 | 9 |
| 3 | 3 |
| 1 |
Prime factors of 54 are 2,3. Prime factorization of 54 in exponential form is:
54 = 21×33
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
Now multiplying the highest exponent prime factors to calculate the LCM of 54 and 63.
LCM(54,63) = 21×33×71
LCM(54,63) = 378
Factors of 54
List of positive integer factors of 54 that divides 54 without a remainder.
1, 2, 3, 6, 9, 18, 27, 54
Factors of 63
List of positive integer factors of 63 that divides 63 without a remainder.
1, 3, 7, 9, 21, 63
Least Common Multiple of 54 and 63 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54 and 63, than apply into the LCM equation.
GCF(54,63) = 9
LCM(54,63) = ( 54 × 63) / 9
LCM(54,63) = 3402 / 9
LCM(54,63) = 378
Properties of LCM 54 and 63
(i) The LCM of 63 and 54 is associative
LCM of 54 and 63 = LCM of 63 and 54
Related Least Common Multiples of 54
Related Least Common Multiples of 63
Frequently Asked Questions on LCM of 54 and 63
1. What is the LCM of 54 and 63?
Answer: LCM of 54 and 63 is 378.
2. What are the Factors of 54?
Answer: Factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54. There are 8 integers that are factors of 54. The greatest factor of 54 is 54.
3. 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.
4. How to Find the LCM of 54 and 63?
Answer:
Least Common Multiple of 54 and 63 = 378
Step 1: Find the prime factorization of 54
54 = 2 x 3 x 3 x 3
Step 2: Find the prime factorization of 63
63 = 3 x 3 x 7
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 378 = 2 x 3 x 3 x 3 x 7
Step 4: Therefore, the least common multiple of 54 and 63 is 378.
