Least Common Multiple (LCM) of 72 and 21
The least common multiple (LCM) of 72 and 21 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 72 and 21?
First, calculate the GCD of 72 and 21 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 21 = 3 remainder 9 |
| 2 | 21 ÷ 9 = 2 remainder 3 |
| 3 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 168 and 176 | 3696 |
| 191 and 47 | 8977 |
| 92 and 143 | 13156 |
| 48 and 31 | 1488 |
| 189 and 199 | 37611 |