Least Common Multiple (LCM) of 96 and 134
The least common multiple (LCM) of 96 and 134 is 6432.
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 96 and 134?
First, calculate the GCD of 96 and 134 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 96 ÷ 134 = 0 remainder 96 |
| 2 | 134 ÷ 96 = 1 remainder 38 |
| 3 | 96 ÷ 38 = 2 remainder 20 |
| 4 | 38 ÷ 20 = 1 remainder 18 |
| 5 | 20 ÷ 18 = 1 remainder 2 |
| 6 | 18 ÷ 2 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 41 and 110 | 4510 |
| 92 and 72 | 1656 |
| 35 and 31 | 1085 |
| 132 and 45 | 1980 |
| 56 and 155 | 8680 |