Least Common Multiple (LCM) of 21 and 72
The least common multiple (LCM) of 21 and 72 is 504.
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 72?
First, calculate the GCD of 21 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 72 = 0 remainder 21 |
| 2 | 72 ÷ 21 = 3 remainder 9 |
| 3 | 21 ÷ 9 = 2 remainder 3 |
| 4 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 151 and 41 | 6191 |
| 61 and 90 | 5490 |
| 96 and 199 | 19104 |
| 187 and 121 | 2057 |
| 110 and 140 | 1540 |