Least Common Multiple (LCM) of 112 and 72
The least common multiple (LCM) of 112 and 72 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 72?
First, calculate the GCD of 112 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 72 = 1 remainder 40 |
| 2 | 72 ÷ 40 = 1 remainder 32 |
| 3 | 40 ÷ 32 = 1 remainder 8 |
| 4 | 32 ÷ 8 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 79 | 3555 |
| 133 and 108 | 14364 |
| 115 and 160 | 3680 |
| 71 and 61 | 4331 |
| 132 and 96 | 1056 |