Least Common Multiple (LCM) of 84 and 133
The least common multiple (LCM) of 84 and 133 is 1596.
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 133?
First, calculate the GCD of 84 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 84 ÷ 133 = 0 remainder 84 |
| 2 | 133 ÷ 84 = 1 remainder 49 |
| 3 | 84 ÷ 49 = 1 remainder 35 |
| 4 | 49 ÷ 35 = 1 remainder 14 |
| 5 | 35 ÷ 14 = 2 remainder 7 |
| 6 | 14 ÷ 7 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 111 and 142 | 15762 |
| 50 and 140 | 700 |
| 169 and 193 | 32617 |
| 33 and 164 | 5412 |
| 176 and 34 | 2992 |