GCF and LCM Calculator
Find the greatest common factor and least common multiple of several whole numbers. Explore equal chunks and repeating cycles with exact counts and steps.
Enter 2–12 positive integers, separated by commas, spaces or new lines. Commas separate numbers: 1,234 means 1 and 234. Each number may have up to 48 digits.
GCF, also called GCD: the largest whole number that divides every input.
LCM: the smallest positive whole number divisible by every input.
Both answers are exact, including large integers.
The first shared finish
Cycles starting together, with intervals of 8, 12, 20, first meet again after 120 units of time. This assumes the same time unit and a common starting point.
The first positive multiple shared by 8, 12 and 20 is 120.
Exact counts for every number
Exact calculation steps
GCF(8, 12) = 4; GCF(4, 20) = 4.
LCM(8, 12) = (8 ÷ 4) × 12 = 24; LCM(24, 20) = (24 ÷ 4) × 20 = 120.
The remainder method finds GCF without listing factors. For two numbers, LCM(a, b) = (a ÷ GCF(a, b)) × b. Apply each method successively to include all numbers. GCF × LCM equals a × b for two numbers; this identity does not generally hold for a longer list.
Which answer do I need?
Use GCF when dividing whole-number quantities into the largest equal chunks with no remainder. For 12, 18 and 30 units, a chunk of 6 fits each amount exactly: 2, 3 and 5 chunks. A larger shared chunk does not fit all three.
Use LCM to find a common denominator or the first shared finish of repeating cycles that start together. Intervals of 8, 12 and 20 minutes meet again after 120 minutes. Different starting offsets require another calculation; this tool assumes all cycles begin at the same time.
For fraction simplification, operations and common denominators, use the fraction calculator.
Input rules and diagram limits
Use positive whole numbers only. Zero, negative numbers, decimals, fractions and scientific notation are not accepted. Spaces, new lines, commas and semicolons separate entries; do not leave empty comma or semicolon entries. Limit: 12 numbers, 48 decimal digits per number and 5,000 characters in the list.
Calculations use exact integers. Diagrams use a shared horizontal scale when every row needs at most 24 marks. Larger counts use an explicitly labeled schematic that omits the repeated middle; every entered number and exact count remain shown below. Diagram positions do not determine the answer.
Method reference: Texas Instruments: Here’s Looking at Euclid.
