Least Common Multiple (LCM) of 134 and 154
The least common multiple (LCM) of 134 and 154 is 10318.
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 134 and 154?
First, calculate the GCD of 134 and 154 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 134 ÷ 154 = 0 remainder 134 |
| 2 | 154 ÷ 134 = 1 remainder 20 |
| 3 | 134 ÷ 20 = 6 remainder 14 |
| 4 | 20 ÷ 14 = 1 remainder 6 |
| 5 | 14 ÷ 6 = 2 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 191 and 50 | 9550 |
| 98 and 113 | 11074 |
| 80 and 65 | 1040 |
| 75 and 29 | 2175 |
| 195 and 112 | 21840 |