# std::lcm

< cpp‎ | numeric

Numerics library
Common mathematical functions
Mathematical special functions (C++17)
Mathematical constants (C++20)
Basic linear algebra algorithms (C++26)
Floating-point environment (C++11)
Complex numbers
Numeric arrays
Pseudo-random number generation
Factor operations
(C++17)
lcm
(C++17)
Interpolations
(C++20)
(C++20)
Saturation arithmetic
 mul_sat(C++26) div_sat(C++26)
Generic numeric operations
 iota(C++11) ranges::iota(C++23) accumulate inner_product adjacent_difference partial_sum
 reduce(C++17) transform_reduce(C++17) inclusive_scan(C++17) exclusive_scan(C++17) transform_inclusive_scan(C++17) transform_exclusive_scan(C++17)
Bit operations
 has_single_bit(C++20) bit_cast(C++20) bit_ceil(C++20) bit_floor(C++20) bit_width(C++20) rotl(C++20) rotr(C++20)
 popcount(C++20) countl_zero(C++20) countl_one(C++20) countr_zero(C++20) countr_one(C++20) byteswap(C++23) endian(C++20)

 Defined in header  template< class M, class N > constexpr std::common_type_t lcm( M m, N n ); (since C++17)

Computes the least common multiple of the integers m and n.

If either M or N is not an integer type, or if either is (possibly cv-qualified) bool, the program is ill-formed.

The behavior is undefined if |m|, |n|, or the least common multiple of |m| and |n| is not representable as a value of type std::common_type_t<M, N>.

## Contents

### Parameters

 m, n - integer values

### Return value

If either m or n is zero, returns zero. Otherwise, returns the least common multiple of |m| and |n|.

### Exceptions

Throws no exceptions.

### Notes

Feature-test macro Value Std Feature
__cpp_lib_gcd_lcm 201606L (C++17) std::gcd, std::lcm

### Example

#include <iostream>
#include <numeric>

#define OUT(...) std::cout << #__VA_ARGS__ << " = " << __VA_ARGS__ << '\n'

constexpr auto lcm(auto x, auto... xs)
{
return ((x = std::lcm(x, xs)), ...);
}

int main()
{
constexpr int p{2 * 2 * 3};
constexpr int q{2 * 3 * 3};
static_assert(2 * 2 * 3 * 3 == std::lcm(p, q));
static_assert(225 == std::lcm(45, 75));

static_assert(std::lcm( 6,  10) == 30);
static_assert(std::lcm( 6, -10) == 30);
static_assert(std::lcm(-6, -10) == 30);

static_assert(std::lcm( 24, 0) == 0);
static_assert(std::lcm(-24, 0) == 0);

OUT(lcm(2 * 3, 3 * 4, 4 * 5));
OUT(lcm(2 * 3 * 4, 3 * 4 * 5, 4 * 5 * 6));
OUT(lcm(2 * 3 * 4, 3 * 4 * 5, 4 * 5 * 6, 5 * 6 * 7));
}

Output:

lcm(2 * 3, 3 * 4, 4 * 5) = 60
lcm(2 * 3 * 4, 3 * 4 * 5, 4 * 5 * 6) = 120
lcm(2 * 3 * 4, 3 * 4 * 5, 4 * 5 * 6, 5 * 6 * 7) = 840