Least Common Multiple (LCM) of 37 and 126
The least common multiple (LCM) of 37 and 126 is 4662.
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 126?
First, calculate the GCD of 37 and 126 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 37 ÷ 126 = 0 remainder 37 |
| 2 | 126 ÷ 37 = 3 remainder 15 |
| 3 | 37 ÷ 15 = 2 remainder 7 |
| 4 | 15 ÷ 7 = 2 remainder 1 |
| 5 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 44 and 33 | 132 |
| 148 and 52 | 1924 |
| 91 and 130 | 910 |
| 86 and 166 | 7138 |
| 141 and 165 | 7755 |