Least Common Multiple (LCM) of 19 and 159
The least common multiple (LCM) of 19 and 159 is 3021.
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 19 and 159?
First, calculate the GCD of 19 and 159 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 19 ÷ 159 = 0 remainder 19 |
| 2 | 159 ÷ 19 = 8 remainder 7 |
| 3 | 19 ÷ 7 = 2 remainder 5 |
| 4 | 7 ÷ 5 = 1 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 40 and 109 | 4360 |
| 136 and 103 | 14008 |
| 161 and 127 | 20447 |
| 135 and 145 | 3915 |
| 70 and 143 | 10010 |