Least Common Multiple (LCM) of 156 and 199
The least common multiple (LCM) of 156 and 199 is 31044.
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 199?
First, calculate the GCD of 156 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 156 ÷ 199 = 0 remainder 156 |
| 2 | 199 ÷ 156 = 1 remainder 43 |
| 3 | 156 ÷ 43 = 3 remainder 27 |
| 4 | 43 ÷ 27 = 1 remainder 16 |
| 5 | 27 ÷ 16 = 1 remainder 11 |
| 6 | 16 ÷ 11 = 1 remainder 5 |
| 7 | 11 ÷ 5 = 2 remainder 1 |
| 8 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 154 and 121 | 1694 |
| 92 and 87 | 8004 |
| 102 and 11 | 1122 |
| 157 and 123 | 19311 |
| 71 and 81 | 5751 |