
Least Common Multiple (LCM) of 74 and 119
The least common multiple (LCM) of 74 and 119 is 8806.
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 74 and 119?
First, calculate the GCD of 74 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
Step | Calculation |
---|---|
1 | 74 ÷ 119 = 0 remainder 74 |
2 | 119 ÷ 74 = 1 remainder 45 |
3 | 74 ÷ 45 = 1 remainder 29 |
4 | 45 ÷ 29 = 1 remainder 16 |
5 | 29 ÷ 16 = 1 remainder 13 |
6 | 16 ÷ 13 = 1 remainder 3 |
7 | 13 ÷ 3 = 4 remainder 1 |
8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
Numbers | LCM |
---|---|
114 and 78 | 1482 |
131 and 46 | 6026 |
189 and 75 | 4725 |
75 and 100 | 300 |
61 and 57 | 3477 |