Least Common Multiple (LCM) of 112 and 74
The least common multiple (LCM) of 112 and 74 is 4144.
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 74?
First, calculate the GCD of 112 and 74 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 74 = 1 remainder 38 |
| 2 | 74 ÷ 38 = 1 remainder 36 |
| 3 | 38 ÷ 36 = 1 remainder 2 |
| 4 | 36 ÷ 2 = 18 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 174 and 170 | 14790 |
| 52 and 48 | 624 |
| 35 and 102 | 3570 |
| 112 and 16 | 112 |
| 46 and 154 | 3542 |