Least Common Multiple (LCM) of 10 and 126
The least common multiple (LCM) of 10 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 10 and 126?
First, calculate the GCD of 10 and 126 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 10 ÷ 126 = 0 remainder 10 |
| 2 | 126 ÷ 10 = 12 remainder 6 |
| 3 | 10 ÷ 6 = 1 remainder 4 |
| 4 | 6 ÷ 4 = 1 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 148 and 124 | 4588 |
| 160 and 100 | 800 |
| 117 and 82 | 9594 |
| 159 and 187 | 29733 |
| 15 and 83 | 1245 |