Least Common Multiple (LCM) of 112 and 42
The least common multiple (LCM) of 112 and 42 is 336.
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 42?
First, calculate the GCD of 112 and 42 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 42 = 2 remainder 28 |
| 2 | 42 ÷ 28 = 1 remainder 14 |
| 3 | 28 ÷ 14 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 11 and 127 | 1397 |
| 34 and 20 | 340 |
| 138 and 120 | 2760 |
| 60 and 63 | 1260 |
| 105 and 102 | 3570 |