Least Common Multiple (LCM) of 21 and 39
The least common multiple (LCM) of 21 and 39 is 273.
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 39?
First, calculate the GCD of 21 and 39 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 39 = 0 remainder 21 |
| 2 | 39 ÷ 21 = 1 remainder 18 |
| 3 | 21 ÷ 18 = 1 remainder 3 |
| 4 | 18 ÷ 3 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 95 and 12 | 1140 |
| 51 and 72 | 1224 |
| 53 and 160 | 8480 |
| 184 and 117 | 21528 |
| 160 and 52 | 2080 |