Math Problem Statement

what is the lcm of 20 and 55

Solution

The Least Common Multiple (LCM) of 20 and 55 is the smallest number that both 20 and 55 divide into without leaving a remainder.

Steps to find the LCM:

  1. Prime Factorization:

    • 20=22×520 = 2^2 \times 5
    • 55=5×1155 = 5 \times 11
  2. LCM Calculation: Take the highest power of each prime factor present in the factorizations.

    • From 20: 222^2 and 55
    • From 55: 55 and 1111

    The LCM is 22×5×11=4×5×11=2202^2 \times 5 \times 11 = 4 \times 5 \times 11 = 220.

Thus, the LCM of 20 and 55 is 220.

Would you like more details or have any questions?

Related Questions:

  1. What is the LCM of 20 and 30?
  2. How do you find the GCD (Greatest Common Divisor) of two numbers?
  3. What is the LCM of 15, 20, and 55?
  4. Can the LCM be smaller than both numbers?
  5. What is the relationship between LCM and GCD?

Tip: The LCM of two numbers is always divisible by both numbers!

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Math Problem Analysis

Mathematical Concepts

Number Theory
Least Common Multiple (LCM)
Prime Factorization

Formulas

LCM(a, b) = (a * b) / GCD(a, b)

Theorems

Prime Factorization

Suitable Grade Level

Grades 5-7