Least Common Multiple (LCM) of 67 and 112
The least common multiple (LCM) of 67 and 112 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 67 and 112?
First, calculate the GCD of 67 and 112 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 112 = 0 remainder 67 |
| 2 | 112 ÷ 67 = 1 remainder 45 |
| 3 | 67 ÷ 45 = 1 remainder 22 |
| 4 | 45 ÷ 22 = 2 remainder 1 |
| 5 | 22 ÷ 1 = 22 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 67 | 1407 |
| 84 and 148 | 3108 |
| 41 and 36 | 1476 |
| 114 and 21 | 798 |
| 67 and 63 | 4221 |