Least Common Multiple (LCM) of 156 and 196
The least common multiple (LCM) of 156 and 196 is 7644.
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 156 and 196?
First, calculate the GCD of 156 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 156 ÷ 196 = 0 remainder 156 |
| 2 | 196 ÷ 156 = 1 remainder 40 |
| 3 | 156 ÷ 40 = 3 remainder 36 |
| 4 | 40 ÷ 36 = 1 remainder 4 |
| 5 | 36 ÷ 4 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 41 and 31 | 1271 |
| 108 and 110 | 5940 |
| 106 and 110 | 5830 |
| 21 and 99 | 693 |
| 183 and 138 | 8418 |