Least Common Multiple (LCM) of 54 and 147
The least common multiple (LCM) of 54 and 147 is 2646.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 54 and 147?
First, calculate the GCD of 54 and 147 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 147 = 0 remainder 54 |
| 2 | 147 ÷ 54 = 2 remainder 39 |
| 3 | 54 ÷ 39 = 1 remainder 15 |
| 4 | 39 ÷ 15 = 2 remainder 9 |
| 5 | 15 ÷ 9 = 1 remainder 6 |
| 6 | 9 ÷ 6 = 1 remainder 3 |
| 7 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 167 and 162 | 27054 |
| 158 and 122 | 9638 |
| 12 and 69 | 276 |
| 60 and 182 | 5460 |
| 167 and 93 | 15531 |