Least Common Multiple (LCM) of 101 and 111
The least common multiple (LCM) of 101 and 111 is 11211.
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 101 and 111?
First, calculate the GCD of 101 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 111 = 0 remainder 101 |
| 2 | 111 ÷ 101 = 1 remainder 10 |
| 3 | 101 ÷ 10 = 10 remainder 1 |
| 4 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 100 | 3600 |
| 138 and 165 | 7590 |
| 51 and 117 | 1989 |
| 148 and 171 | 25308 |
| 189 and 131 | 24759 |