GCF, LCM of 45, 75, 90
Answer (1)
Answer:To find the Greatest Common Factor (GCF) and Least Common Multiple (LCM) of 45, 75, and 90, let's break them down into their prime factors:Prime Factorization: * 45 = 3 * 3 * 5 * 75 = 3 * 5 * 5 * 90 = 2 * 3 * 3 * 5GCF:The GCF is the product of the common prime factors raised to the lowest power they appear in any of the numbers. * Common prime factors: 3 and 5 * Lowest powers: 3^1 (in 45) and 5^1 (in 45)GCF = 3 * 5 = 15LCM:The LCM is the product of all prime factors raised to the highest power they appear in any of the numbers. * Prime factors: 2, 3, and 5 * Highest powers: 2^1 (in 90), 3^2 (in 45 and 90), and 5^2 (in 75)LCM = 2 * 3^2 * 5^2 = 2 * 9 * 25 = 450Therefore, the GCF of 45, 75, and 90 is 15, and the LCM is 450.
