Least Common Multiple (LCM) of 21 and 16
The least common multiple (LCM) of 21 and 16 is 336.
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 16?
First, calculate the GCD of 21 and 16 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 16 = 1 remainder 5 |
| 2 | 16 ÷ 5 = 3 remainder 1 |
| 3 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 198 and 112 | 11088 |
| 114 and 83 | 9462 |
| 167 and 138 | 23046 |
| 170 and 38 | 3230 |
| 79 and 137 | 10823 |