Least Common Multiple (LCM) of 45 and 126
The least common multiple (LCM) of 45 and 126 is 630.
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 126?
First, calculate the GCD of 45 and 126 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 126 = 0 remainder 45 |
| 2 | 126 ÷ 45 = 2 remainder 36 |
| 3 | 45 ÷ 36 = 1 remainder 9 |
| 4 | 36 ÷ 9 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 52 and 155 | 8060 |
| 194 and 72 | 6984 |
| 114 and 192 | 3648 |
| 112 and 85 | 9520 |
| 185 and 80 | 2960 |