Least Common Multiple (LCM) of 162 and 200
The least common multiple (LCM) of 162 and 200 is 16200.
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 162 and 200?
First, calculate the GCD of 162 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 162 ÷ 200 = 0 remainder 162 |
| 2 | 200 ÷ 162 = 1 remainder 38 |
| 3 | 162 ÷ 38 = 4 remainder 10 |
| 4 | 38 ÷ 10 = 3 remainder 8 |
| 5 | 10 ÷ 8 = 1 remainder 2 |
| 6 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 96 and 129 | 4128 |
| 60 and 188 | 2820 |
| 132 and 175 | 23100 |
| 114 and 54 | 1026 |
| 33 and 115 | 3795 |