Least Common Multiple (LCM) of 154 and 53
The least common multiple (LCM) of 154 and 53 is 8162.
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 154 and 53?
First, calculate the GCD of 154 and 53 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 154 ÷ 53 = 2 remainder 48 |
| 2 | 53 ÷ 48 = 1 remainder 5 |
| 3 | 48 ÷ 5 = 9 remainder 3 |
| 4 | 5 ÷ 3 = 1 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 16 and 78 | 624 |
| 177 and 79 | 13983 |
| 193 and 44 | 8492 |
| 162 and 130 | 10530 |
| 63 and 110 | 6930 |