Least Common Multiple (LCM) of 102 and 154
The least common multiple (LCM) of 102 and 154 is 7854.
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 102 and 154?
First, calculate the GCD of 102 and 154 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 154 = 0 remainder 102 |
| 2 | 154 ÷ 102 = 1 remainder 52 |
| 3 | 102 ÷ 52 = 1 remainder 50 |
| 4 | 52 ÷ 50 = 1 remainder 2 |
| 5 | 50 ÷ 2 = 25 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 105 | 11235 |
| 90 and 129 | 3870 |
| 21 and 173 | 3633 |
| 75 and 113 | 8475 |
| 17 and 111 | 1887 |