Least Common Multiple (LCM) of 159 and 138
The least common multiple (LCM) of 159 and 138 is 7314.
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 159 and 138?
First, calculate the GCD of 159 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 159 ÷ 138 = 1 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 |
|---|---|
| 155 and 129 | 19995 |
| 123 and 14 | 1722 |
| 153 and 70 | 10710 |
| 100 and 75 | 300 |
| 143 and 192 | 27456 |