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lcm

Calculates the least common multiple (LCM) of two numbers with precision handling. Computes the smallest positive number that is divisible by both input numbers. Supports both integers and decimal numbers by handling floating-point precision issues appropriately. Uses the mathematical relationship: LCM(a,b) = |a×b| / GCD(a,b).

Signature​

const lcm: (left: number, right: number) => number

Parameters​

NameTypeDescription
left-First number (integer or decimal)
right-Second number (integer or decimal)

Returns​

Least common multiple of the two numbers

Examples​

Integer LCM calculations​

import { lcm } from '@winglet/common-utils';

console.log(lcm(12, 8)); // 24 (smallest number divisible by both 12 and 8)
console.log(lcm(15, 25)); // 75
console.log(lcm(7, 11)); // 77 (coprime numbers: LCM = product)
console.log(lcm(6, 9)); // 18
console.log(lcm(100, 50)); // 100

Decimal and edge case handling​

// Decimal numbers (with precision handling)
console.log(lcm(1.2, 0.8)); // 2.4 (LCM with proper decimal precision)
console.log(lcm(2.5, 1.5)); // 7.5

// Edge cases
console.log(lcm(0, 5)); // 0 (LCM with zero)
console.log(lcm(7, 0)); // 0 (LCM with zero)
console.log(lcm(-12, 8)); // 24 (absolute values used)
console.log(lcm(-6, -9)); // 18 (absolute values used)

Playground​

import { lcm } from '@winglet/common-utils';

console.log(lcm(12, 8)); // 24 (smallest number divisible by both 12 and 8)
console.log(lcm(15, 25)); // 75
console.log(lcm(7, 11)); // 77 (coprime numbers: LCM = product)
console.log(lcm(6, 9)); // 18
console.log(lcm(100, 50)); // 100

Notes​

Mathematical Properties:

  • lcm(a, 0) = 0 for any number a
  • lcm(a, b) = lcm(b, a) (commutative)
  • lcm(a, b) = lcm(|a|, |b|) (sign independent)
  • For coprime numbers: lcm(a, b) = |a × b|
  • Always returns a non-negative result

Use Cases:

  • Finding common denominators for fraction arithmetic
  • Synchronizing periodic events or cycles
  • Algorithm optimization requiring common intervals
  • Time scheduling and resource allocation
  • Digital signal processing (sample rate conversion)
  • Mathematical computations requiring common multiples

Performance: O(log(min(a, b))) time complexity due to GCD calculation. Space complexity is O(1). Includes precision handling for decimal inputs.