Least Common Multiple (LCM) of 105 and 126
The least common multiple (LCM) of 105 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 105 and 126?
First, calculate the GCD of 105 and 126 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 126 = 0 remainder 105 |
| 2 | 126 ÷ 105 = 1 remainder 21 |
| 3 | 105 ÷ 21 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 134 and 37 | 4958 |
| 136 and 44 | 1496 |
| 76 and 86 | 3268 |
| 95 and 133 | 665 |
| 14 and 72 | 504 |