To find the multiple of 3, 11, and 22 that is less than 100, we need to find the LCM. To find the LCM, we need to look for prime factors that are common to either 2 or 3 of them. To start to do this, we must first find the prime factorization of each of these numbers. Since 3 and 11 are prime, the prime factorizations of them are 3 and 11 respectively. The prime factorization of 22 is 11 * 2. Since 11 is shared by both 11 and 22, we can take it out. Since none of the other numbers are shared, wee can just put them. That means that the answer is: 11 * 2 * 3 = 22 * 3 = 66.
