This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1892 Excerpt: ... common multiple is multiplied or divided by this number. Cor. 3. The product of two numbers is the product of their highest common measure and lowest common multiple. COMMON MEASURES AND MULTIPLES OF THREE NUMBERS. Theor. 15. The highest common measure of three numbers is the highest common measure of the highest ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1892 Excerpt: ... common multiple is multiplied or divided by this number. Cor. 3. The product of two numbers is the product of their highest common measure and lowest common multiple. COMMON MEASURES AND MULTIPLES OF THREE NUMBERS. Theor. 15. The highest common measure of three numbers is the highest common measure of the highest common measure of any two of the numbers and the third number; and so for the lowest common multiple. COMMON MEASURES AND MULTIPLES OF TWO FRACTIONS. Theor. 16. The highest common measure of two fractions in their lowest terms is the quotient of the highest common measure of the numerators by the lowest common multiple of the denominators; and their lowest common multiple is the quotient of the lowest common multiple of the numerators by the highest common measure of the denominators. For, let A/b, C/d be two fractions in their lowest terms, and let F/m be a measure of them in its lowest terms; then v A/b: F/m, C/d.: F/m, i.e., Am/bf, Cm/df are entire, /. F is a common measure of A, C, and M a common multiple of B, D; th. 4 cr. 2, th. 9 cr. 2. and F/m is highest when F is the highest common measure of A, c, and M the lowest common multiple of B, D., So, let M/f be a common multiple of A/b, C/d; then v M/f: A/b, M/f: C/d, i.e., Bm/af, Dm/cf are entire, .. F is a common measure of B, D, and M a common multiple of A, c, th. 4 cr. 2, th. 9 cr. 2. and M/f is lowest when F is the highest common measure of B, D, and M the lowest common multiple of A, C. Questions. 1. In the proof of theor. 14, show that each of the numbers is a measure of such a product, and that, if any factor were omitted from this product or taken fewer times, some one of the numbers would no longer be a measure of it. 2. In the lowest common multiple of A, b, what factors of A are fou..
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