Least Common Multiple (LCM) of 42 and 118
The least common multiple (LCM) of 42 and 118 is 2478.
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 42 and 118?
First, calculate the GCD of 42 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 42 ÷ 118 = 0 remainder 42 |
| 2 | 118 ÷ 42 = 2 remainder 34 |
| 3 | 42 ÷ 34 = 1 remainder 8 |
| 4 | 34 ÷ 8 = 4 remainder 2 |
| 5 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 191 and 14 | 2674 |
| 38 and 24 | 456 |
| 28 and 144 | 1008 |
| 112 and 26 | 1456 |
| 105 and 178 | 18690 |