Least Common Multiple (LCM) of 111 and 21
The least common multiple (LCM) of 111 and 21 is 777.
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 111 and 21?
First, calculate the GCD of 111 and 21 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 21 = 5 remainder 6 |
| 2 | 21 ÷ 6 = 3 remainder 3 |
| 3 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 45 | 1710 |
| 38 and 58 | 1102 |
| 121 and 78 | 9438 |
| 23 and 154 | 3542 |
| 89 and 179 | 15931 |