Least Common Multiple (LCM) of 42 and 56
The least common multiple (LCM) of 42 and 56 is 168.
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 56?
First, calculate the GCD of 42 and 56 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 42 ÷ 56 = 0 remainder 42 |
| 2 | 56 ÷ 42 = 1 remainder 14 |
| 3 | 42 ÷ 14 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 22 and 55 | 110 |
| 179 and 34 | 6086 |
| 68 and 84 | 1428 |
| 122 and 126 | 7686 |
| 54 and 160 | 4320 |