Least Common Multiple (LCM) of 156 and 114
The least common multiple (LCM) of 156 and 114 is 2964.
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 156 and 114?
First, calculate the GCD of 156 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 156 ÷ 114 = 1 remainder 42 |
| 2 | 114 ÷ 42 = 2 remainder 30 |
| 3 | 42 ÷ 30 = 1 remainder 12 |
| 4 | 30 ÷ 12 = 2 remainder 6 |
| 5 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 200 | 25800 |
| 197 and 114 | 22458 |
| 172 and 71 | 12212 |
| 22 and 188 | 2068 |
| 197 and 141 | 27777 |