Least Common Multiple (LCM) of 21 and 159
The least common multiple (LCM) of 21 and 159 is 1113.
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 159?
First, calculate the GCD of 21 and 159 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 159 = 0 remainder 21 |
| 2 | 159 ÷ 21 = 7 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 |
|---|---|
| 125 and 77 | 9625 |
| 135 and 166 | 22410 |
| 130 and 52 | 260 |
| 35 and 122 | 4270 |
| 160 and 85 | 2720 |