Least Common Multiple (LCM) of 23 and 153
The least common multiple (LCM) of 23 and 153 is 3519.
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 23 and 153?
First, calculate the GCD of 23 and 153 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 23 ÷ 153 = 0 remainder 23 |
| 2 | 153 ÷ 23 = 6 remainder 15 |
| 3 | 23 ÷ 15 = 1 remainder 8 |
| 4 | 15 ÷ 8 = 1 remainder 7 |
| 5 | 8 ÷ 7 = 1 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 130 | 4290 |
| 135 and 52 | 7020 |
| 156 and 54 | 1404 |
| 122 and 180 | 10980 |
| 200 and 19 | 3800 |