Least Common Multiple (LCM) of 102 and 74
The least common multiple (LCM) of 102 and 74 is 3774.
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 74?
First, calculate the GCD of 102 and 74 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 74 = 1 remainder 28 |
| 2 | 74 ÷ 28 = 2 remainder 18 |
| 3 | 28 ÷ 18 = 1 remainder 10 |
| 4 | 18 ÷ 10 = 1 remainder 8 |
| 5 | 10 ÷ 8 = 1 remainder 2 |
| 6 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 152 and 78 | 5928 |
| 117 and 171 | 2223 |
| 60 and 99 | 1980 |
| 49 and 171 | 8379 |
| 192 and 77 | 14784 |