Least Common Multiple (LCM) of 20 and 72
The least common multiple (LCM) of 20 and 72 is 360.
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 20 and 72?
First, calculate the GCD of 20 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 20 ÷ 72 = 0 remainder 20 |
| 2 | 72 ÷ 20 = 3 remainder 12 |
| 3 | 20 ÷ 12 = 1 remainder 8 |
| 4 | 12 ÷ 8 = 1 remainder 4 |
| 5 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 73 and 140 | 10220 |
| 114 and 83 | 9462 |
| 21 and 193 | 4053 |
| 172 and 132 | 5676 |
| 15 and 98 | 1470 |