Least Common Multiple (LCM) of 100 and 22
The least common multiple (LCM) of 100 and 22 is 1100.
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 100 and 22?
First, calculate the GCD of 100 and 22 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 22 = 4 remainder 12 |
| 2 | 22 ÷ 12 = 1 remainder 10 |
| 3 | 12 ÷ 10 = 1 remainder 2 |
| 4 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 13 and 21 | 273 |
| 159 and 106 | 318 |
| 34 and 179 | 6086 |
| 199 and 159 | 31641 |
| 149 and 46 | 6854 |