ACT Math: GCF and LCM—Find Them Fast and Use Them Wisely

GCF (greatest common factor) is the largest number that divides evenly into two or more numbers. Example: GCF of 12 and 18 is 6 (since 6 divides both and no larger number does). LCM (least common multiple) is the smallest number that both numbers divide into evenly. Example: LCM of 4 and 6 is 12 (since both 4 and 6 divide into 12 with no remainder, and no smaller number works). On the ACT, you use GCF to simplify fractions (12/18 reduces to 2/3 using GCF=6) and to factor polynomials. You use LCM to add fractions (common denominator), solve systems with fractions, or word problems involving cycles. Know both concepts and recognize instantly which problem type needs which tool.

Quick method: To find GCF, list factors of both numbers and pick the largest. To find LCM, list multiples of the larger number until one is also a multiple of the smaller.

Error 1: Confusing GCF and LCM (GCF is smaller; LCM is larger). Error 2: Forgetting that 1 is always a common factor, so GCF is at least 1. Error 3: For LCM, stopping too early. "Multiples of 6: 6, 12, 18..." but forgetting to check if the other number divides evenly. Error 4: Finding GCF of only the first pair of numbers in a multi-number problem and forgetting to include the third. After finding GCF or LCM, verify: Does your GCF divide both numbers? Does both numbers divide into your LCM?

Checklist: (1) Identify whether the problem needs simplification (GCF) or a common denominator (LCM). (2) List factors (GCF) or multiples (LCM). (3) Pick the largest factor or smallest multiple. (4) Check your answer by dividing or multiplying. (5) Write the final answer clearly.

Pair 1: 15 and 20. GCF=5, LCM=60. Pair 2: 8 and 12. GCF=4, LCM=24. Pair 3: 9 and 27. GCF=9, LCM=27. Pair 4: 14 and 35. GCF=7, LCM=70. Pair 5: 6, 10, and 15. GCF=1, LCM=30. Pair 6: 12 and 18. GCF=6, LCM=36. For Pair 5, verify: 1 divides all three, and 30 is divisible by 6, 10, and 15. Check yourself this way every time.

Drill: Each day, pick five random pairs of numbers and find both GCF and LCM. Time yourself: you should finish all five in under two minutes once you're fast.

These are foundational skills. Questions using GCF and LCM are usually in the easier-to-medium range, meaning they're worth the same points but feel simpler if you know the method. A fraction simplification question or a word problem about cycles is essentially a GCF/LCM question in disguise. Mastering these two concepts lets you solve problems fast without confusion, freeing up time for harder questions that require more conceptual thinking.

Spend three days drilling GCF and LCM until they feel automatic. That investment returns time and confidence during the test.