Least Common Multiple (LCM) of 84 and 134
The least common multiple (LCM) of 84 and 134 is 5628.
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 84 and 134?
First, calculate the GCD of 84 and 134 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 84 ÷ 134 = 0 remainder 84 |
| 2 | 134 ÷ 84 = 1 remainder 50 |
| 3 | 84 ÷ 50 = 1 remainder 34 |
| 4 | 50 ÷ 34 = 1 remainder 16 |
| 5 | 34 ÷ 16 = 2 remainder 2 |
| 6 | 16 ÷ 2 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 144 | 720 |
| 142 and 16 | 1136 |
| 63 and 100 | 6300 |
| 29 and 33 | 957 |
| 70 and 42 | 210 |