Least Common Multiple (LCM) of 37 and 69
The least common multiple (LCM) of 37 and 69 is 2553.
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 69?
First, calculate the GCD of 37 and 69 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 37 ÷ 69 = 0 remainder 37 |
| 2 | 69 ÷ 37 = 1 remainder 32 |
| 3 | 37 ÷ 32 = 1 remainder 5 |
| 4 | 32 ÷ 5 = 6 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 16 | 240 |
| 199 and 112 | 22288 |
| 123 and 197 | 24231 |
| 45 and 22 | 990 |
| 191 and 110 | 21010 |