Least Common Multiple (LCM) of 153 and 165
The least common multiple (LCM) of 153 and 165 is 8415.
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 153 and 165?
First, calculate the GCD of 153 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 153 ÷ 165 = 0 remainder 153 |
| 2 | 165 ÷ 153 = 1 remainder 12 |
| 3 | 153 ÷ 12 = 12 remainder 9 |
| 4 | 12 ÷ 9 = 1 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 75 and 135 | 675 |
| 91 and 198 | 18018 |
| 194 and 105 | 20370 |
| 61 and 51 | 3111 |
| 173 and 60 | 10380 |