Least Common Multiple (LCM) of 100 and 134
The least common multiple (LCM) of 100 and 134 is 6700.
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 100 and 134?
First, calculate the GCD of 100 and 134 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 134 = 0 remainder 100 |
| 2 | 134 ÷ 100 = 1 remainder 34 |
| 3 | 100 ÷ 34 = 2 remainder 32 |
| 4 | 34 ÷ 32 = 1 remainder 2 |
| 5 | 32 ÷ 2 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 49 and 146 | 7154 |
| 27 and 76 | 2052 |
| 185 and 179 | 33115 |
| 180 and 181 | 32580 |
| 54 and 116 | 3132 |