Least Common Multiple (LCM) of 13 and 153
The least common multiple (LCM) of 13 and 153 is 1989.
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 13 and 153?
First, calculate the GCD of 13 and 153 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 13 ÷ 153 = 0 remainder 13 |
| 2 | 153 ÷ 13 = 11 remainder 10 |
| 3 | 13 ÷ 10 = 1 remainder 3 |
| 4 | 10 ÷ 3 = 3 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 93 and 81 | 2511 |
| 189 and 103 | 19467 |
| 173 and 30 | 5190 |
| 88 and 11 | 88 |
| 52 and 179 | 9308 |