Least Common Multiple (LCM) of 102 and 134
The least common multiple (LCM) of 102 and 134 is 6834.
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 134?
First, calculate the GCD of 102 and 134 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 134 = 0 remainder 102 |
| 2 | 134 ÷ 102 = 1 remainder 32 |
| 3 | 102 ÷ 32 = 3 remainder 6 |
| 4 | 32 ÷ 6 = 5 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 172 and 93 | 15996 |
| 19 and 145 | 2755 |
| 138 and 39 | 1794 |
| 45 and 178 | 8010 |
| 151 and 121 | 18271 |