Least Common Multiple (LCM) of 22 and 101
The least common multiple (LCM) of 22 and 101 is 2222.
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 22 and 101?
First, calculate the GCD of 22 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 22 ÷ 101 = 0 remainder 22 |
| 2 | 101 ÷ 22 = 4 remainder 13 |
| 3 | 22 ÷ 13 = 1 remainder 9 |
| 4 | 13 ÷ 9 = 1 remainder 4 |
| 5 | 9 ÷ 4 = 2 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 85 and 48 | 4080 |
| 100 and 186 | 9300 |
| 147 and 10 | 1470 |
| 122 and 85 | 10370 |
| 154 and 67 | 10318 |