Least Common Multiple (LCM) of 54 and 77
The least common multiple (LCM) of 54 and 77 is 4158.
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 77?
First, calculate the GCD of 54 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 77 = 0 remainder 54 |
| 2 | 77 ÷ 54 = 1 remainder 23 |
| 3 | 54 ÷ 23 = 2 remainder 8 |
| 4 | 23 ÷ 8 = 2 remainder 7 |
| 5 | 8 ÷ 7 = 1 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 10 and 68 | 340 |
| 180 and 70 | 1260 |
| 199 and 126 | 25074 |
| 42 and 31 | 1302 |
| 32 and 129 | 4128 |