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Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
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3, 7.6 आणि 0.13 या संख्यांचा लसावि (LCM) किती आहे?
102
100
107
98.8
102
Convert decimals to fractions with a common denominator (e.g., denominators of 100), then find the LCM of the numerators and divide by the common denominator.
Three numbers are given as 1.3, 7.6, and 0.13.
LCM(ba,dc,fe)=HCF(b,d,f)LCM(a,c,e)
Convert decimals to fractions with a common denominator (e.g., denominators of 100), then find the LCM of the numerators and divide by the common denominator.
Students often find the LCM of the decimals directly as if they were integers or forget to equalize decimal places, leading to incorrect placement of the decimal point.
Convert decimals to fractions
To make calculation easy, express numbers as fractions with the same denominator. 1.3 = 130/100, 7.6 = 760/100, 0.13 = 13/100.
100130,100760,10013
Apply LCM formula for fractions
The LCM of fractions is the LCM of the numerators divided by the HCF of the denominators.
LCM=HCF(100,100,100)LCM(130,760,13)
Calculate LCM of numerators
Prime factorization: 130 = 2 × 5 × 13; 760 = 2³ × 5 × 19; 13 = 13. LCM = 2³ × 5 × 13 × 19 = 8 × 5 × 13 × 19 = 9880.
LCM(130,760,13)=9880
Calculate HCF of denominators
The denominators are all 100, so the HCF is simply 100.
HCF(100,100,100)=100
Final division
Divide the numerator LCM by the denominator HCF: 9880 / 100 = 98.8.
1009880=98.8
D is correct because the LCM of 1.3, 7.6, and 0.13 is 98.8.
This concept of fraction-based LCM is frequently used in HCF/LCM problems involving units (e.g., converting meters to cm) and ratio-based arithmetic.