Least Common Multiple (LCM) of 113 and 21
The least common multiple (LCM) of 113 and 21 is 2373.
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 113 and 21?
First, calculate the GCD of 113 and 21 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 21 = 5 remainder 8 |
| 2 | 21 ÷ 8 = 2 remainder 5 |
| 3 | 8 ÷ 5 = 1 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 161 and 84 | 1932 |
| 172 and 120 | 5160 |
| 115 and 150 | 3450 |
| 107 and 180 | 19260 |
| 187 and 66 | 1122 |