Least Common Multiple (LCM) of 100 and 35
The least common multiple (LCM) of 100 and 35 is 700.
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 100 and 35?
First, calculate the GCD of 100 and 35 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 35 = 2 remainder 30 |
| 2 | 35 ÷ 30 = 1 remainder 5 |
| 3 | 30 ÷ 5 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 101 | 10403 |
| 153 and 47 | 7191 |
| 24 and 145 | 3480 |
| 175 and 26 | 4550 |
| 144 and 112 | 1008 |