To find the least common multiple (LCM) of 7.56 and 5, we first express the numbers in a form that’s easier to work with. A common approach is to convert the decimal into a fraction.
7.56 can be expressed as 756/100. Next, we can simplify this fraction. Both the numerator and denominator can be divided by 4, giving us 189/25. Now we have two fractions: 189/25 and 5, which we can express as 5/1.
Now, to find the LCM, we first need the denominators to be the same. We see that the LCM of the denominators (25 and 1) is 25. We can rewrite 5 as 125/25 to have a common denominator.
Now, our two fractions are 189/25 and 125/25. The LCM of the numerators (189 and 125) can be calculated by finding the highest multiple of each number that both can share. The prime factorization of 189 is 3^3 * 7, while the prime factorization of 125 is 5^3. Since these numbers share no common factors, we can multiply them directly to find the LCM of the numerators, which is 189 * 125.
Calculating this gives us 23625. Now, since we have the common denominator of 25, we place our LCM over that denominator: LCM = 23625/25.
Now, simplifying this division, we find that the LCM is 945. Thus, the LCM of 7.56 and 5 is 945.