Least Common Multiple (LCM) of 117 and 159
The least common multiple (LCM) of 117 and 159 is 6201.
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 117 and 159?
First, calculate the GCD of 117 and 159 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 159 = 0 remainder 117 |
| 2 | 159 ÷ 117 = 1 remainder 42 |
| 3 | 117 ÷ 42 = 2 remainder 33 |
| 4 | 42 ÷ 33 = 1 remainder 9 |
| 5 | 33 ÷ 9 = 3 remainder 6 |
| 6 | 9 ÷ 6 = 1 remainder 3 |
| 7 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 105 | 3990 |
| 135 and 77 | 10395 |
| 111 and 170 | 18870 |
| 131 and 27 | 3537 |
| 160 and 111 | 17760 |