Least Common Multiple (LCM) of 126 and 112
The least common multiple (LCM) of 126 and 112 is 1008.
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 112?
First, calculate the GCD of 126 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 112 = 1 remainder 14 |
| 2 | 112 ÷ 14 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 111 and 176 | 19536 |
| 35 and 21 | 105 |
| 196 and 103 | 20188 |
| 197 and 77 | 15169 |
| 67 and 108 | 7236 |