Least Common Multiple (LCM) of 112 and 63
The least common multiple (LCM) of 112 and 63 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 112 and 63?
First, calculate the GCD of 112 and 63 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 63 = 1 remainder 49 |
| 2 | 63 ÷ 49 = 1 remainder 14 |
| 3 | 49 ÷ 14 = 3 remainder 7 |
| 4 | 14 ÷ 7 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 16 and 56 | 112 |
| 122 and 136 | 8296 |
| 70 and 200 | 1400 |
| 176 and 49 | 8624 |
| 151 and 80 | 12080 |