Least Common Multiple (LCM) of 76 and 200
The least common multiple (LCM) of 76 and 200 is 3800.
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 76 and 200?
First, calculate the GCD of 76 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 76 ÷ 200 = 0 remainder 76 |
| 2 | 200 ÷ 76 = 2 remainder 48 |
| 3 | 76 ÷ 48 = 1 remainder 28 |
| 4 | 48 ÷ 28 = 1 remainder 20 |
| 5 | 28 ÷ 20 = 1 remainder 8 |
| 6 | 20 ÷ 8 = 2 remainder 4 |
| 7 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 125 | 14000 |
| 92 and 87 | 8004 |
| 183 and 182 | 33306 |
| 165 and 156 | 8580 |
| 172 and 98 | 8428 |