# Number Theory LCM

> Number Theory LCM is a paid API for AI agents from numtheory.openverbs.com, paid per call via x402, $0.004/call, status unknown (last checked 2026-09-15).

Computes the Least Common Multiple (LCM) of two or more non-negative integers supplied as decimal strings

## Facts

- Endpoint: POST https://numtheory.openverbs.com/v1/lcm
- Price: $0.004/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-15
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/number-theory-lcm-502c3e47
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_uGgMeRIMzE6W6blrjeUEd

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability number-theory-lcm-502c3e47 -d '<json body>'
```

Example prompt: What is the least common multiple of 12, 18, and 24?

## When to prefer this

Choose this endpoint when you need a reliable, pay-per-call computation of the LCM of two to 256 integers without running your own math service. It is ideal for agents handling dynamic scheduling, fraction arithmetic, or periodic synchronization problems where the operand count or size varies at runtime.

## Known failure modes

- Input array has fewer than 2 elements — rejected with validation error
- Values contain non-numeric or negative strings — rejected due to pattern constraint
- More than 256 values supplied — rejected due to maxItems constraint
- Network or payment authorization failure — HTTP 402 or 5xx response

## How this service works

Least common multiple of two or more positive integers (arbitrary precision).

## Output

Returns the least common multiple of all provided integers as a numeric value, representing the smallest positive integer evenly divisible by every number in the input list.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "$schema": "https://json-schema.org/draft/2020-12/schema",
 "required": [
  "input"
 ],
 "properties": {
  "input": {
   "type": "object",
   "required": [
    "type",
    "method",
    "bodyType",
    "body"
   ],
   "properties": {
    "body": {
     "type": "object",
     "required": [
      "values"
     ],
     "properties": {
      "values": {
       "type": "array",
       "items": {
        "type": "string",
        "pattern": "^\\d+$"
       },
       "maxItems": 256,
       "minItems": 2,
       "description": "Two or more non-negative integers as decimal strings."
      }
     },
     "additionalProperties": false
    },
    "type": {
     "type": "string",
     "const": "http"
    },
    "method": {
     "enum": [
      "POST"
     ],
     "type": "string"
    },
    "bodyType": {
     "enum": [
      "json",
      "form-data",
      "text"
     ],
     "type": "string"
    }
   },
   "additionalProperties": false
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/number-theory-lcm-502c3e47/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from numtheory.openverbs.com](https://www.zero.xyz/host/numtheory.openverbs.com/llms.txt)