Least Common Multiple (LCM) of 107 and 154
The least common multiple (LCM) of 107 and 154 is 16478.
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 107 and 154?
First, calculate the GCD of 107 and 154 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 154 = 0 remainder 107 |
| 2 | 154 ÷ 107 = 1 remainder 47 |
| 3 | 107 ÷ 47 = 2 remainder 13 |
| 4 | 47 ÷ 13 = 3 remainder 8 |
| 5 | 13 ÷ 8 = 1 remainder 5 |
| 6 | 8 ÷ 5 = 1 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 39 and 81 | 1053 |
| 118 and 180 | 10620 |
| 110 and 159 | 17490 |
| 116 and 96 | 2784 |
| 112 and 33 | 3696 |