Least Common Multiple (LCM) of 200 and 105
The least common multiple (LCM) of 200 and 105 is 4200.
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 200 and 105?
First, calculate the GCD of 200 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 200 ÷ 105 = 1 remainder 95 |
| 2 | 105 ÷ 95 = 1 remainder 10 |
| 3 | 95 ÷ 10 = 9 remainder 5 |
| 4 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 156 and 113 | 17628 |
| 156 and 62 | 4836 |
| 52 and 110 | 2860 |
| 149 and 24 | 3576 |
| 11 and 65 | 715 |