Least Common Multiple (LCM) of 37 and 87
The least common multiple (LCM) of 37 and 87 is 3219.
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 87?
First, calculate the GCD of 37 and 87 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 37 ÷ 87 = 0 remainder 37 |
| 2 | 87 ÷ 37 = 2 remainder 13 |
| 3 | 37 ÷ 13 = 2 remainder 11 |
| 4 | 13 ÷ 11 = 1 remainder 2 |
| 5 | 11 ÷ 2 = 5 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 78 | 8814 |
| 190 and 200 | 3800 |
| 40 and 40 | 40 |
| 107 and 153 | 16371 |
| 43 and 134 | 5762 |