Least Common Multiple (LCM) of 35 and 60
The least common multiple (LCM) of 35 and 60 is 420.
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 60?
First, calculate the GCD of 35 and 60 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 35 ÷ 60 = 0 remainder 35 |
| 2 | 60 ÷ 35 = 1 remainder 25 |
| 3 | 35 ÷ 25 = 1 remainder 10 |
| 4 | 25 ÷ 10 = 2 remainder 5 |
| 5 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 117 | 16614 |
| 195 and 51 | 3315 |
| 81 and 100 | 8100 |
| 82 and 79 | 6478 |
| 199 and 90 | 17910 |