Least Common Multiple (LCM) of 112 and 67
The least common multiple (LCM) of 112 and 67 is 7504.
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 67?
First, calculate the GCD of 112 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 67 = 1 remainder 45 |
| 2 | 67 ÷ 45 = 1 remainder 22 |
| 3 | 45 ÷ 22 = 2 remainder 1 |
| 4 | 22 ÷ 1 = 22 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 28 and 30 | 420 |
| 59 and 11 | 649 |
| 166 and 180 | 14940 |
| 76 and 82 | 3116 |
| 73 and 144 | 10512 |