Least Common Multiple (LCM) of 21 and 45
The least common multiple (LCM) of 21 and 45 is 315.
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 21 and 45?
First, calculate the GCD of 21 and 45 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 45 = 0 remainder 21 |
| 2 | 45 ÷ 21 = 2 remainder 3 |
| 3 | 21 ÷ 3 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 131 and 105 | 13755 |
| 186 and 59 | 10974 |
| 111 and 101 | 11211 |
| 60 and 138 | 1380 |
| 39 and 104 | 312 |