Least Common Multiple (LCM) of 21 and 138
The least common multiple (LCM) of 21 and 138 is 966.
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 138?
First, calculate the GCD of 21 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 138 = 0 remainder 21 |
| 2 | 138 ÷ 21 = 6 remainder 12 |
| 3 | 21 ÷ 12 = 1 remainder 9 |
| 4 | 12 ÷ 9 = 1 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 147 and 136 | 19992 |
| 16 and 121 | 1936 |
| 195 and 190 | 7410 |
| 52 and 190 | 4940 |
| 117 and 172 | 20124 |