Least Common Multiple (LCM) of 105 and 153
The least common multiple (LCM) of 105 and 153 is 5355.
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 105 and 153?
First, calculate the GCD of 105 and 153 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 153 = 0 remainder 105 |
| 2 | 153 ÷ 105 = 1 remainder 48 |
| 3 | 105 ÷ 48 = 2 remainder 9 |
| 4 | 48 ÷ 9 = 5 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 49 | 5635 |
| 80 and 81 | 6480 |
| 140 and 166 | 11620 |
| 145 and 170 | 4930 |
| 89 and 141 | 12549 |