Least Common Multiple (LCM) of 134 and 49
The least common multiple (LCM) of 134 and 49 is 6566.
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 49?
First, calculate the GCD of 134 and 49 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 134 ÷ 49 = 2 remainder 36 |
| 2 | 49 ÷ 36 = 1 remainder 13 |
| 3 | 36 ÷ 13 = 2 remainder 10 |
| 4 | 13 ÷ 10 = 1 remainder 3 |
| 5 | 10 ÷ 3 = 3 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 156 and 47 | 7332 |
| 145 and 97 | 14065 |
| 23 and 107 | 2461 |
| 89 and 78 | 6942 |
| 105 and 105 | 105 |