Least Common Multiple (LCM) of 21 and 99
The least common multiple (LCM) of 21 and 99 is 693.
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 99?
First, calculate the GCD of 21 and 99 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 99 = 0 remainder 21 |
| 2 | 99 ÷ 21 = 4 remainder 15 |
| 3 | 21 ÷ 15 = 1 remainder 6 |
| 4 | 15 ÷ 6 = 2 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 139 and 112 | 15568 |
| 135 and 45 | 135 |
| 56 and 31 | 1736 |
| 102 and 36 | 612 |
| 116 and 101 | 11716 |