Least Common Multiple (LCM) of 35 and 188
The least common multiple (LCM) of 35 and 188 is 6580.
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 35 and 188?
First, calculate the GCD of 35 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 35 ÷ 188 = 0 remainder 35 |
| 2 | 188 ÷ 35 = 5 remainder 13 |
| 3 | 35 ÷ 13 = 2 remainder 9 |
| 4 | 13 ÷ 9 = 1 remainder 4 |
| 5 | 9 ÷ 4 = 2 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 113 | 12430 |
| 17 and 105 | 1785 |
| 85 and 106 | 9010 |
| 117 and 10 | 1170 |
| 160 and 97 | 15520 |