LCM means “meet again”
Use it when several repeating patterns must align: denominators, schedules, gears, beats, or equal-size batches.
CALCULATE · SEE THE METHOD · PRACTICE
LCM Calculator
Find the least common multiple of 2–20 positive integers, then prove the answer through prime powers, multiples, ladder/division work, the GCF identity, and a two-number factor overlap.
20numbers at once
6solution views
exactinteger math
LEAST COMMON MULTIPLE LAB
One LCM, six ways to understand it
Inputs use exact BigInt arithmetic. Each input is limited to unsigned 64-bit so prime-factor proofs remain deterministic; the resulting LCM may be larger.
LEAST COMMON MULTIPLE180
LCM(12, 18, 30) = 180
GCF6
prime powers used3
smallest common multipleverified
PRIME FACTORIZATION
2² × 3² × 5 = 180Keep the highest exponent of every prime
LISTING MULTIPLES
first shared = 180Find the first number shared by every list
CAKE / LADDER METHOD
LCM = 180Divide shared factors, then multiply the L-shape
DIVISION METHOD
LCM = 180Divide by primes until every value reaches 1
USING THE GCF
exact identityReduce pairwise with a × b ÷ GCF(a,b)
TWO-NUMBER FACTOR OVERLAP
best with 2 inputsShared factors sit in the middle; the LCM uses the whole union
LOWEST COMMON DENOMINATOR
Turn unlike fractions into like fractions
The LCD is the LCM of the denominators.
LCD24
4/24, 15/24, 14/24
REPEATING SCHEDULES
When will the cycles line up again?
If events repeat every fixed number of equal time units, their first simultaneous repeat is the LCM.
together again after120 minutes
120 is divisible by 6, 8, and 15.
DECIMAL LCM
Scale decimals exactly, then scale back
No floating-point approximation: decimal strings are converted to integers using the maximum number of decimal places.
decimal LCM3.6
Scale ×100 → LCM(120, 18) = 360 → 3.6
DAILY 12
Build LCM instincts
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LCM
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FOCUSED PRACTICE
Train exactly the pattern you need
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MIXED
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30sHighest prime powers win
Prime-factorize each input. For every prime that appears anywhere, keep the greatest exponent seen.
LCM vs GCF
GCF asks for the biggest number dividing every input. LCM asks for the smallest positive number divisible by every input.
Two-number shortcut
For positive integers a and b: LCM(a,b) × GCF(a,b) = a × b.
LOCAL HISTORY
Your recent LCMs
Stored only in this browser.
Methods, exactness & scope
Exact integer arithmetic
Inputs, GCF, LCM, ladder rows, equivalent fractions, and schedule intervals use JavaScript BigInt with no floating-point rounding.
Deterministic factor proofs
Prime-factor views use deterministic Miller–Rabin plus Pollard-rho within the declared unsigned 64-bit input range.
Why positive integers?
This page focuses on the standard classroom definition of the least positive common multiple. Decimal inputs are intentionally excluded rather than silently changing scale.
Large answers
The LCM can exceed 64-bit even though each input cannot. BigInt preserves the exact result; very large visual listings are intentionally shortened.