Least Common Multiple (LCM) of 60 and 102
The least common multiple (LCM) of 60 and 102 is 1020.
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 60 and 102?
First, calculate the GCD of 60 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 60 ÷ 102 = 0 remainder 60 |
| 2 | 102 ÷ 60 = 1 remainder 42 |
| 3 | 60 ÷ 42 = 1 remainder 18 |
| 4 | 42 ÷ 18 = 2 remainder 6 |
| 5 | 18 ÷ 6 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 104 and 52 | 104 |
| 33 and 51 | 561 |
| 193 and 96 | 18528 |
| 149 and 90 | 13410 |
| 128 and 174 | 11136 |