Least Common Multiple (LCM) of 54 and 176
The least common multiple (LCM) of 54 and 176 is 4752.
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 176?
First, calculate the GCD of 54 and 176 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 176 = 0 remainder 54 |
| 2 | 176 ÷ 54 = 3 remainder 14 |
| 3 | 54 ÷ 14 = 3 remainder 12 |
| 4 | 14 ÷ 12 = 1 remainder 2 |
| 5 | 12 ÷ 2 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 172 and 19 | 3268 |
| 153 and 157 | 24021 |
| 42 and 97 | 4074 |
| 120 and 65 | 1560 |
| 109 and 66 | 7194 |