Least Common Multiple (LCM) of 54 and 172
The least common multiple (LCM) of 54 and 172 is 4644.
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 172?
First, calculate the GCD of 54 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 172 = 0 remainder 54 |
| 2 | 172 ÷ 54 = 3 remainder 10 |
| 3 | 54 ÷ 10 = 5 remainder 4 |
| 4 | 10 ÷ 4 = 2 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 183 | 8418 |
| 105 and 112 | 1680 |
| 29 and 53 | 1537 |
| 63 and 50 | 3150 |
| 125 and 19 | 2375 |