Least Common Multiple (LCM) of 153 and 65
The least common multiple (LCM) of 153 and 65 is 9945.
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 65?
First, calculate the GCD of 153 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 153 ÷ 65 = 2 remainder 23 |
| 2 | 65 ÷ 23 = 2 remainder 19 |
| 3 | 23 ÷ 19 = 1 remainder 4 |
| 4 | 19 ÷ 4 = 4 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 183 and 109 | 19947 |
| 32 and 172 | 1376 |
| 51 and 117 | 1989 |
| 122 and 119 | 14518 |
| 158 and 148 | 11692 |