Least Common Multiple (LCM) of 55 and 156
The least common multiple (LCM) of 55 and 156 is 8580.
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 55 and 156?
First, calculate the GCD of 55 and 156 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 55 ÷ 156 = 0 remainder 55 |
| 2 | 156 ÷ 55 = 2 remainder 46 |
| 3 | 55 ÷ 46 = 1 remainder 9 |
| 4 | 46 ÷ 9 = 5 remainder 1 |
| 5 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 51 and 72 | 1224 |
| 30 and 129 | 1290 |
| 66 and 11 | 66 |
| 35 and 194 | 6790 |
| 188 and 172 | 8084 |