Least Common Multiple (LCM) of 45 and 156
The least common multiple (LCM) of 45 and 156 is 2340.
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 45 and 156?
First, calculate the GCD of 45 and 156 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 156 = 0 remainder 45 |
| 2 | 156 ÷ 45 = 3 remainder 21 |
| 3 | 45 ÷ 21 = 2 remainder 3 |
| 4 | 21 ÷ 3 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 75 | 2550 |
| 42 and 184 | 3864 |
| 119 and 20 | 2380 |
| 72 and 114 | 1368 |
| 117 and 38 | 4446 |