Least Common Multiple (LCM) of 55 and 134
The least common multiple (LCM) of 55 and 134 is 7370.
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 55 and 134?
First, calculate the GCD of 55 and 134 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 55 ÷ 134 = 0 remainder 55 |
| 2 | 134 ÷ 55 = 2 remainder 24 |
| 3 | 55 ÷ 24 = 2 remainder 7 |
| 4 | 24 ÷ 7 = 3 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 90 and 130 | 1170 |
| 79 and 175 | 13825 |
| 107 and 67 | 7169 |
| 49 and 51 | 2499 |
| 77 and 164 | 12628 |