Least Common Multiple (LCM) of 37 and 142
The least common multiple (LCM) of 37 and 142 is 5254.
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 37 and 142?
First, calculate the GCD of 37 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 37 ÷ 142 = 0 remainder 37 |
| 2 | 142 ÷ 37 = 3 remainder 31 |
| 3 | 37 ÷ 31 = 1 remainder 6 |
| 4 | 31 ÷ 6 = 5 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 54 and 150 | 1350 |
| 49 and 180 | 8820 |
| 129 and 126 | 5418 |
| 197 and 140 | 27580 |
| 48 and 199 | 9552 |