Least Common Multiple (LCM) of 154 and 83
The least common multiple (LCM) of 154 and 83 is 12782.
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 154 and 83?
First, calculate the GCD of 154 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 154 ÷ 83 = 1 remainder 71 |
| 2 | 83 ÷ 71 = 1 remainder 12 |
| 3 | 71 ÷ 12 = 5 remainder 11 |
| 4 | 12 ÷ 11 = 1 remainder 1 |
| 5 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 127 and 108 | 13716 |
| 113 and 68 | 7684 |
| 48 and 27 | 432 |
| 197 and 120 | 23640 |
| 79 and 119 | 9401 |