Least Common Multiple (LCM) of 126 and 45
The least common multiple (LCM) of 126 and 45 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 126 and 45?
First, calculate the GCD of 126 and 45 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 45 = 2 remainder 36 |
| 2 | 45 ÷ 36 = 1 remainder 9 |
| 3 | 36 ÷ 9 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 118 and 171 | 20178 |
| 160 and 101 | 16160 |
| 127 and 13 | 1651 |
| 107 and 194 | 20758 |
| 97 and 74 | 7178 |