Ratios, Proportions, Percentages, Fractions

LCM, GCF, Prime Numbers

2020 June(C02) Math Question 1

2012 December(71A) Math Question 2

2020 July(C01) Math Question 3

3. What is the least common denominator of the fractions

Least Common Multiple (LCM)

2021 June(D06) Math Question 3

2010 December(69A) Math Question 5

6. What is the least common multiple of 60, 70, and 90 ?

2020 December(D03) Math Question 6

2019 June(72F) Math Question 7

7. What is the least common multiple of 50, 70, and 90 ?

2015 April(73G) Math Question 7

9. Let a and 17 be positive prime numbers. Which of the following numbers must be a factor of both a and b ?

2013 June(71C) Math Question 9

2013 April(71G) Math Question 10

2011 April(67F) Math Question 10

2018 December(B05) Math Question 11

2013 December(71E) Math Question 12

2009 April(66F) Math Question 12

2019 April(B04) Math Question 12

2019 December(C03) Math Question 15

2009 June(67C) Math Question 16

2010 April(68G) Math Question 18

2010 June(68C) Math Question 20

23. One welcome sign flashes every 8 seconds, and another welcome sign flashes every 12 seconds. At a certain instant, the 2 signs flash at the same time. How many seconds elapse until the 2 signs next flash at the same time?

2021 December(E23) Math Question 23

2011 June(69F) Math Question 24

24. The set of all positive integers that are divisible by both 15 and 35 is infinite. What is the least positive integer in this set?

2021 April(Z04) Math Question 24

28. A cash prize will be given to the winning group of the talent show at Aspen High School. The winning group will receive a cash prize that, when divided equally among the students in that group, gives each student in the group a whole-dollar share of the prize. Considering that a group of 2, 3, 4, or 5 students could win the show, what is the least possible amount that the cash prize can be?

2015 December(72E) Math Question 28

31. The number 1,001 is the product of the prime numbers 7, 11, and 13. Knowing this, what is the prime factorization of 30,030 ?

2017 April(74F) Math Question 31

34. Given that n is a positive integer and b is 3 times n, what is the least common denominator, in terms of n. for the addition of 1/b and 1/n ?

2015 December(72E) Math Question 34

2020 July(C01) Math Question 34

37. Consider all products xy such that x is divisible by 8 and y is divisible by 14. Which of the following whole numbers is NOT a factor of each product xy ?

2015 April(73G) Math Question 37

37. For all real numbers x such that x # 0, 4 7.; + 7 — = ?

2017 June(74C) Math Question 37

2019 April(Z15) Math Question 39

2019 December(C03) Math Question 39

39. The only factor that is common to 200 and an integer n is 1. When n/210 is written as a decimal number, what is the minimum number of digits to the right of the decimal point?

2014 April(71H) Math Question 39

2012 April(70G) Math Question 40

41. For all x not equal to —2, which of the following expressions is equal to (x2 + 5x + 6)/(x + 2) + x + 5 ?

2016 April(73E) Math Question 41

2012 April(70G) Math Question 44

47. The least common multiple (LCM) of 2 numbers is 108. The greater of the 2 numbers is 54. What is the maximum value of the other number?

2014 April(71H) Math Question 47

47. The greatest common factor of 2 whole numbers is 10. The least common multiple of these same 2 numbers is 120. What are the 2 numbers?

2017 June(74C) Math Question 47

2012 April(70G) Math Question 47

2014 June(72C) Math Question 47

2018 April(A09) Math Question 49

2018 December(B05) Math Question 50

2011 June(69F) Math Question 50

50. Let a be a prime number greater than 10,000 and let x = square root of a. Which of the following expressions represents a rational number?

2015 December(72E) Math Question 50

54. How many integers between, but not including, 20 and
30 have a prime factorization with exactly 3 factors
that are NOT necessarily unique?
(Note: 1 is NOT a prime number.)

2019 June(B02) Math Question 54

57. Consider the fractions 1/a, 1/b, and 1/c, where a and b are distinct prime numbers greater than 3 and c = 3a. Suppose that a•b•c is used as the common denominator when finding the sum of these fractions. In order for the sum to be in lowest terms, its numerator and denominator must be reduced by a factor of which of the following?
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LCM, GCF, Prime NumbersRatios, Proportions, Percentages, FractionsACT math questions

2020 June(C02) Math Question 1

2012 December(71A) Math Question 2