4/5, 1/2, 9/10, 3/4
To find the LCM of 5, 2, 10, and 4, we start by writing their prime factorizations. We will color each factor differently to help us with the next step.
5 = & 5
2 = & 2
10 = & 2 * 5
4 = & 2 * 2
Next, we multiply the prime factors, being sure to include each unique prime factor only once.
5* 2 * 2 = 20
Equivalent Fractions
We want to find fractions with a denominator of 20 that are equivalent to the given fractions. Let's start with 45. We multiply 5 by 4 to get 20, so we will also multiply 4 by 4 to get its equivalent fraction.
We found that 1620 is equivalent to 45. Let's consider 12 next. We multiply 2 by 10 to get 20, so we will also multiply 1 by 10 to get our equivalent fraction.
We found that 1020 is equivalent to 15. Next, let's find an equivalent fraction for 910. This time we will multiply the numerator and denominator by 2.
Our fraction that is equivalent to 910 is 1820. Finally, we will rewrite 34 to have a denominator of 20. We multiply 4 by 5 to get 20, so we will also multiply 3 by 5 to get our equivalent fraction.
The final equivalent fraction is 1520.
Comparing the Numerators
Let's write all the equivalent fractions and consider their numerators.
Original Fraction
Equivalent Fraction
4/5
16/20
1/2
10/20
9/10
18/20
3/4
15/20
To order the fractions with the same denominator from least to greatest, we order the numerators from least to greatest.
