Least Common Multiple (LCM) of 153 and 83
The least common multiple (LCM) of 153 and 83 is 12699.
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 83?
First, calculate the GCD of 153 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 153 ÷ 83 = 1 remainder 70 |
| 2 | 83 ÷ 70 = 1 remainder 13 |
| 3 | 70 ÷ 13 = 5 remainder 5 |
| 4 | 13 ÷ 5 = 2 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 146 and 35 | 5110 |
| 74 and 67 | 4958 |
| 180 and 134 | 12060 |
| 28 and 188 | 1316 |
| 16 and 53 | 848 |