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Fast Calculation of HCF and LCM
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13 Sep 2024, 02:03
13 Sep 2024, 02:03
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This is part of our GRE Math Essentials - A most comprehensive handout!!! is the best complement to our GRE Math Book. It provides a cutting-edge, in-depth overview of all the math concepts from basic to mid-upper levels. The book still remains our hallmark: from basic to the most advanced GRE math concepts tested during the exam. Moreover, the following chapters will give you many tips, tricks, and shortcuts to make your quant preparation more robust and solid.
Fast Calculation of HCF and LCM
Example 1: Numbers 72 and 108
Write the numbers side by side: x = 72, y = 108
Factor out the common terms: 72, 108 (Divide both by 12)
This gives: 6,9 (Divide both by 3) 2,3 (No common factor left)
HCF:
The common factors are 12 × 3 = 36.
Hence, the HCF is 36
LCM:
Multiply the HCF by the remaining non-common factors: LCM = 36 × 2 × 3 = 216
When there are only 2 numbers, then x * y = HCF * LCM (this holds true ONLY when there are 2 numbers).
Example 2: Numbers 12, 15, 18, 30
Write the numbers side by side: 12, 15, 18, 30
Factor out the common terms:
12, 15, 18, 30 (Divide all by 3)
4,5,6,10 (No common factor left)
HCF:
The common factor is 3. Hence, HCF = 3.
For LCM, continue dividing by partially common factors
4,5,6,10 (Divide 4, 6, 10 by 2)
2,5,3,5 (Divide 5, 5, by 5)
2,1,3,1 (No common factor left)
LCM:
Multiply all the common factors by the remaining non-common factors:
LCM = 3 × 2 × 5 × 2 × 3 = 180
Fast Calculation of HCF and LCM
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13 Sep 2024, 02:09
13 Sep 2024, 02:09
Expert Reply
Thank you sir to post this useful trick or shortcut.
gmatclubot
Fast Calculation of HCF and LCM [#permalink]
13 Sep 2024, 02:09
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