Least Common Multiple (LCM) of 55 and 200
The least common multiple (LCM) of 55 and 200 is 2200.
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 55 and 200?
First, calculate the GCD of 55 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 55 ÷ 200 = 0 remainder 55 |
| 2 | 200 ÷ 55 = 3 remainder 35 |
| 3 | 55 ÷ 35 = 1 remainder 20 |
| 4 | 35 ÷ 20 = 1 remainder 15 |
| 5 | 20 ÷ 15 = 1 remainder 5 |
| 6 | 15 ÷ 5 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 129 | 17673 |
| 51 and 108 | 1836 |
| 77 and 12 | 924 |
| 141 and 70 | 9870 |
| 129 and 169 | 21801 |