Least Common Multiple (LCM) of 84 and 50
The least common multiple (LCM) of 84 and 50 is 2100.
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 50?
First, calculate the GCD of 84 and 50 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 84 ÷ 50 = 1 remainder 34 |
| 2 | 50 ÷ 34 = 1 remainder 16 |
| 3 | 34 ÷ 16 = 2 remainder 2 |
| 4 | 16 ÷ 2 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 28 and 17 | 476 |
| 47 and 64 | 3008 |
| 105 and 119 | 1785 |
| 151 and 21 | 3171 |
| 134 and 20 | 1340 |