Least Common Multiple (LCM) of 159 and 196
The least common multiple (LCM) of 159 and 196 is 31164.
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 159 and 196?
First, calculate the GCD of 159 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 159 ÷ 196 = 0 remainder 159 |
| 2 | 196 ÷ 159 = 1 remainder 37 |
| 3 | 159 ÷ 37 = 4 remainder 11 |
| 4 | 37 ÷ 11 = 3 remainder 4 |
| 5 | 11 ÷ 4 = 2 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 78 | 546 |
| 38 and 62 | 1178 |
| 98 and 64 | 3136 |
| 104 and 118 | 6136 |
| 49 and 67 | 3283 |