{
    "name": "Least Common Multiple Calculator",
    "url": "https://calculators.geekmidst.com/calculators/least-common-multiple-calculator",
    "markdown": "https://calculators.geekmidst.com/calculators/least-common-multiple-calculator.md",
    "category": "Mathematics",
    "description": "Find the least common multiple of up to 50 whole numbers, exactly even when it is huge, with each number’s prime factorisation shown.",
    "summary": "The least common multiple is the smallest positive number that every number in the list divides into evenly. It is the lowest common denominator for adding fractions.",
    "also_called": [
        "LCM calculator",
        "Lowest common multiple calculator",
        "LCD calculator"
    ],
    "applies_to": "Worldwide",
    "last_updated": "2026-10-29",
    "computation": "Results are computed in the visitor’s browser on the HTML page. This API describes the calculator; it does not compute results.",
    "inputs": [
        {
            "name": "numbers",
            "label": "Whole numbers",
            "type": "textarea",
            "default": "12, 15, 20"
        }
    ],
    "outputs": [
        {
            "key": "lcm",
            "label": "Least common multiple",
            "format": "text"
        },
        {
            "key": "lcm_factors",
            "label": "LCM as prime factors",
            "format": "text"
        },
        {
            "key": "gcf",
            "label": "Greatest common factor",
            "format": "integer"
        }
    ],
    "formula": {
        "text": "LCM = product of each prime raised to its highest power in any of the numbers;  for two numbers, LCM(a, b) = a × b ÷ GCF(a, b)",
        "variables": {
            "GCF": "greatest common factor"
        }
    },
    "worked_example": {
        "inputs": {
            "numbers": "12, 15, 20"
        },
        "steps": [
            "12 = 2² × 3, 15 = 3 × 5, 20 = 2² × 5.",
            "Take each prime at its highest power: 2², 3¹ and 5¹.",
            "LCM = 4 × 3 × 5 = 60."
        ],
        "result": "The least common multiple of 12, 15 and 20 is 60."
    },
    "interpretation": "To add 1/12 + 1/15 + 1/20, rewrite each fraction over 60. In scheduling, events that repeat every 12, 15 and 20 days coincide every 60 days.",
    "assumptions": [
        "Positive whole numbers up to 1,000,000,000,000."
    ],
    "limitations": [],
    "rules": null,
    "faqs": [
        {
            "question": "What is the difference between LCM and GCF?",
            "answer": "The LCM is the smallest number all of them divide into; the GCF is the largest number that divides all of them. For two numbers, LCM × GCF = a × b."
        },
        {
            "question": "Is the LCM ever smaller than the largest number?",
            "answer": "No. It is at least as large as the largest number, and equals it when the largest is a multiple of all the others."
        }
    ],
    "sources": [],
    "related": [
        {
            "name": "Greatest Common Factor Calculator",
            "url": "https://calculators.geekmidst.com/calculators/greatest-common-factor-calculator"
        },
        {
            "name": "Prime Factorization Calculator",
            "url": "https://calculators.geekmidst.com/calculators/prime-factorization-calculator"
        },
        {
            "name": "Fraction Calculator",
            "url": "https://calculators.geekmidst.com/calculators/fraction-calculator"
        },
        {
            "name": "Common Factor Calculator",
            "url": "https://calculators.geekmidst.com/calculators/common-factor-calculator"
        }
    ],
    "disclaimer": null,
    "publisher": "GM¹X CalcVerse"
}