Least Common Multiple (LCM) of 37 and 196
The least common multiple (LCM) of 37 and 196 is 7252.
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 196?
First, calculate the GCD of 37 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 37 ÷ 196 = 0 remainder 37 |
| 2 | 196 ÷ 37 = 5 remainder 11 |
| 3 | 37 ÷ 11 = 3 remainder 4 |
| 4 | 11 ÷ 4 = 2 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 130 and 96 | 6240 |
| 170 and 48 | 4080 |
| 200 and 29 | 5800 |
| 194 and 47 | 9118 |
| 85 and 103 | 8755 |