You can calculate the least common multiple of two or more monomials by using the factorization method. Get the factors of numerical coefficients and literal coefficients. From the factors, observe the least common multiples and multiply them. And find the product of the lowest common multiples of numerical and literal coefficients of monomials. Have a look at the sample example questions on Lowest Common Multiple of Monomials by Factorization in the below sections.

Example Questions on LCM of Monomials

Example 1:

What is the least common multiple of 5x³y² and 7x²y³?

Solution:

5x³y² = 5 * x * x * x * y * y

7x²y³ = 7 * x * x * y * y * y

From the resolved factors of the above two monomials, the common factors are x, x, y, y.

The extra factors in the first monomial are 5 and in the second monomial are 7, y.

Therefore, the required L.C.M. = Common factors among two monomials × Extra common factors among two monomials.

= (x * x * y * y) x (5 * 7 * y)

= 35x²y³

Hence, the lowest common multiple of the monomials 5x³y² and 7x²y³ = 35x²y³.

Example 2:

Find the L.C.M of 14xy, 21y², 28y.

Solution:

The L.C.M. of numerical coefficients = The L.C.M. of 14, 21, and 28.

Since, 14 = 2 * 7, 21 = 7 * 3, and 28 = 2 * 2 * 7

Therefore, the L.C.M. of 14, 21 and 28 is 2 * 7 * 2 * 3 = 84

The L.C.M. of literal coefficients = The L.C.M. of xy, y², and y = xy²

Since, in xy, y², and y

The highest power of x is 1.

The highest power of y is 2.

Therefore, the L.C.M. of xy, y², and y = xy².

Thus, the L.C.M. of 14xy, 21y², 28y

= The L.C.M. of numerical coefficients × The L.C.M. of literal coefficients

= 84 × (xy²)

= 84xy²

Example 3:

Find the L.C.M of 27u⁴, 18u², 27u².

Solution:

The L.C.M. of numerical coefficients = The L.C.M. of 27, 18, and 27.

Since, 27 = 3 * 3 * 3, 18 = 3 * 3 * 2, 27 = 3 * 3 * 3

Therefore, the L.C.M. of 27, 18, and 27 is 2 * 3 * 3 * 3 = 54

The L.C.M. of literal coefficients = The L.C.M. of u⁴, u², u² = u⁴

Since, in u⁴, u², u²

The highest power of u is 4.

Therefore, the L.C.M. of u⁴, u², u² = u⁴.

Thus, the L.C.M. of 27u⁴, 18u², 27u²

= The L.C.M. of numerical coefficients × The L.C.M. of literal coefficients

= 54 × (u⁴)

= 54u⁴

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