The Least usual Multiple A lot of of a number is a totality number times that number. For example, some multiples that 6 space 6, 12, 18, 24, 30, and also 36 If 2 numbers are given then a common multiple that the 2 numbers is a number that is a multiple of both. Of all the typical multiples of 2 numbers, there is a smallest one i m sorry we contact the least usual multiple. Example uncover the least usual multiple of 6 and 9. Solution One method of addressing this problem is to write out multiples of each and also see what is typical to the list: 6, 12, 18, 24, 30, 36, ... Multiples the 6 9, 18, 27, 36, 45, ... Multiples of 9 We check out that the number 18 and 36 room both usual multiples of 6 and also 9. The least common multiple is the smallest which is 18. Example discover the least typical multiple that 8 and also 32. Solution rather of listing countless multiples of each, we just notice that 32 is a lot of of 8 and also hence 32 is a common multiple. The is the very first multiple that 32. We deserve to conclude that 32 is the least typical multiple of 8 and 32. In general, the least common multiple of 2 numbers with one the lot of of the other is just the bigger number. Exercise uncover the least usual multiple that 15 and also 54. organize mouse end the yellow rectangle for the equipment find the least common multiple that 9 and 81. host mouse over the yellow rectangle for the systems together you observed from the practice A, composing out plenty of multiples of each number have the right to be tedious. There is an alternate an approach that might save time. The strategy is based on the complying with idea. A lot of of a number is a multiple of every of the element divisors.

Steps in finding the LCM create the prime factorization of each number perform the primes that happen in at the very least one the the factorizations form a product using each element the greatest variety of time it occurs in any kind of one the the expressions example Find the LCM the 45 and also 21 equipment 45 = 9 x 5 = 3 x 3 x 5 21 = 3 x 7 3, 5, and also 7 3 x 3 x 5 x 7 The prime 3 occurs 2 times as it does in 3 x 3 x 5 = 9 x 5 x 7 = 45 x 7 = 315 practice find the LCM of

18 and also 40 host mouse over the yellow rectangle because that the systems 12 and 15 hold mouse end the yellow rectangle for the equipment 27 and 10 hold mouse over the yellow rectangle because that the solution The Least typical Denominator We define the least typical denominator of 2 fractions as the least usual multiples of the denominators. Examples discover the least usual denominator of 3/4 and 9/10 5/6 and 10/11 Solutions We find the least typical multiples that 4 and also 10 4 = 2 x 2 10 = 2 x 5 for this reason the least usual denominator is 2 x 2 x 5 = 20 We uncover the least typical multiples the 6 and 11 6 = 2 x 3 11 is element so the least typical denominator is 2 x 3 x 11 = 66 Exercises uncover the least typical denominator the 3/14 and also 2/63 hold mouse end the yellow rectangle for the systems 8/25 and also 23/100 hold mouse over the yellow rectangle for the solution building Up Fractions through a Least usual Denominator us have already learned exactly how to simplify a portion by separating through by a common factor. Occasionally it is practically to be able to work this process in reverse. Example build up the portion to price the inquiry 5 ? = 6 24 Solution We see that 24 = 6 x 4 for this reason 5 5 x 4 20 = = 6 6 x 4 24 Exercise develop up the portion to answer the question 3 ? = 7 35 organize mouse end the yellow rectangle for the systems Example which number is larger: 5/8 or 9/14? Solution because the denominators space different, this numbers are difficult to compare. Our strategy is to construct up each fraction to fractions v the least usual denominator. We an initial find the least typical denominator: 8 = 2 x 2 x 2 14 = 2 x 7 The least usual denominator is 2 x 2 x 2 x 7 = 56 The following step is to notification that 8 x 7 = 56 and also 14 x 4 = 56 We compose 5 5 x 7 35 = = 8 8 x 7 56 and 9 9 x 4 36 = = 14 14 x 4 56 since 35 36 56 56 we conclude that 5 9 8 14 Exercise i beg your pardon is larger: 3/10 or 7/25? host mouse end the yellow rectangle for the systems instance compose the three fractions 1/6, 5/8 and also 3/10 as identical fractions v the LCD as the denominators.

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We have 6 = 2 x 3 8 = 2 x 2 x 2 10 = 2 x 5 so the least usual denominator is 2 x 2 x 2 x 3 x 5 = 8 x 3 x 5 = 24 x 5 = 120 We create 1 1 x 20 20 = = 6 6 x 20 120 5 5 x 15 75 = = 8 8 x 15 120 3 3 x 12 36 = = 10 10 x 12 120 Exercise compose the three fractions 2/15, 4/9 and also 3/25 as tantamount fractions through the LCD together the denominators. host mouse end the yellow rectangle because that the systems back to the fountain page