Two numbers are in the ratio 5: 6 and their sum is 44. Find their least common multiple.
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Jawaban:
Let the two numbers be 5x and 6x, since they are in the ratio 5:6.
Their sum is 5x + 6x = 11x, which is equal to 44. Therefore, x = 4.
So the two numbers are 5x = 20 and 6x = 24.
The prime factorization of 20 is 2^2 * 5, and the prime factorization of 24 is 2^3 * 3. The least common multiple (LCM) of two numbers is the product of the highest powers of all the prime factors that appear in either number.
So the LCM of 20 and 24 is 2^3 * 3 * 5 = 120.
Therefore, the least common multiple of the two numbers is 120.