Least Common Multiple (LCM) of 54 and 156
The least common multiple (LCM) of 54 and 156 is 1404.
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 156?
First, calculate the GCD of 54 and 156 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 156 = 0 remainder 54 |
| 2 | 156 ÷ 54 = 2 remainder 48 |
| 3 | 54 ÷ 48 = 1 remainder 6 |
| 4 | 48 ÷ 6 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 162 and 83 | 13446 |
| 110 and 188 | 10340 |
| 193 and 111 | 21423 |
| 43 and 179 | 7697 |
| 85 and 62 | 5270 |