Least Common Multiple (LCM) of 21 and 31
The least common multiple (LCM) of 21 and 31 is 651.
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 31?
First, calculate the GCD of 21 and 31 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 31 = 0 remainder 21 |
| 2 | 31 ÷ 21 = 1 remainder 10 |
| 3 | 21 ÷ 10 = 2 remainder 1 |
| 4 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 176 and 128 | 1408 |
| 137 and 132 | 18084 |
| 31 and 176 | 5456 |
| 99 and 135 | 1485 |
| 93 and 176 | 16368 |