Least Common Multiple (LCM) of 126 and 105
The least common multiple (LCM) of 126 and 105 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 105?
First, calculate the GCD of 126 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 105 = 1 remainder 21 |
| 2 | 105 ÷ 21 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 133 and 121 | 16093 |
| 52 and 58 | 1508 |
| 102 and 193 | 19686 |
| 105 and 58 | 6090 |
| 103 and 167 | 17201 |